diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index afabb64529..89565b4cb3 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -11882,6 +11882,249 @@ run_test    "TLS 1.3 G->m HRR both with middlebox compat support" \
             -s "tls13 server state: MBEDTLS_SSL_SERVER_CCS_AFTER_HELLO_RETRY_REQUEST" \
             -c "SSL 3.3 ChangeCipherSpec packet received"
 
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check signature algorithm order, m->O" \
+            "$O_NEXT_SRV_NO_CERT -cert data_files/server2-sha256.crt -key data_files/server2.key
+                                 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache
+                                 -Verify 10 -sigalgs rsa_pkcs1_sha512:rsa_pss_rsae_sha512:rsa_pss_rsae_sha384:ecdsa_secp256r1_sha256" \
+            "$P_CLI debug_level=4 crt_file=data_files/server2-sha256.crt key_file=data_files/server2.key \
+                    min_version=tls12 max_version=tls13 sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256" \
+            0 \
+            -c "Protocol is TLSv1.3" \
+            -c "select_sig_alg_for_certificate_verify:selected signature algorithm rsa_pss_rsae_sha512" \
+            -c "HTTP/1.0 200 [Oo][Kk]"
+
+requires_gnutls_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check signature algorithm order, m->G" \
+            "$G_NEXT_SRV_NO_CERT --x509certfile data_files/server2-sha256.crt --x509keyfile data_files/server2.key
+                    -d 4
+                    --priority=NORMAL:-VERS-ALL:-SIGN-ALL:+SIGN-RSA-SHA512:+SIGN-RSA-PSS-RSAE-SHA512:+SIGN-RSA-PSS-RSAE-SHA384:+VERS-TLS1.3:+CIPHER-ALL:%NO_TICKETS " \
+            "$P_CLI debug_level=4 crt_file=data_files/server2-sha256.crt key_file=data_files/server2.key \
+                    min_version=tls12 max_version=tls13 sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256" \
+            0 \
+            -c "Protocol is TLSv1.3" \
+            -c "select_sig_alg_for_certificate_verify:selected signature algorithm rsa_pss_rsae_sha512" \
+            -c "HTTP/1.0 200 [Oo][Kk]"
+
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check signature algorithm order, m->m" \
+            "$P_SRV debug_level=4 force_version=tls13 auth_mode=required
+                    crt_file2=data_files/server2-sha256.crt key_file2=data_files/server2.key
+                    crt_file=data_files/server5.crt key_file=data_files/server5.key
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256 " \
+            "$P_CLI debug_level=4 crt_file=data_files/server2-sha256.crt key_file=data_files/server2.key \
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256 \
+                    min_version=tls12 max_version=tls13 " \
+            0 \
+            -c "Protocol is TLSv1.3" \
+            -c "select_sig_alg_for_certificate_verify:selected signature algorithm rsa_pss_rsae_sha512" \
+            -s "select_sig_alg_for_certificate_verify:selected signature algorithm rsa_pss_rsae_sha512" \
+            -s "ssl_tls13_pick_key_cert:selected signature algorithm rsa_pss_rsae_sha512" \
+            -c "HTTP/1.0 200 [Oo][Kk]"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check signature algorithm order, O->m" \
+            "$P_SRV debug_level=4 force_version=tls13 auth_mode=required
+                    crt_file2=data_files/server2-sha256.crt key_file2=data_files/server2.key
+                    crt_file=data_files/server5.crt key_file=data_files/server5.key
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256 " \
+            "$O_NEXT_CLI_NO_CERT -msg -CAfile data_files/test-ca_cat12.crt \
+                                 -cert data_files/server2-sha256.crt -key data_files/server2.key \
+                                 -sigalgs rsa_pkcs1_sha512:rsa_pss_rsae_sha512:rsa_pss_rsae_sha384:ecdsa_secp256r1_sha256"  \
+            0 \
+            -c "TLSv1.3" \
+            -s "select_sig_alg_for_certificate_verify:selected signature algorithm rsa_pss_rsae_sha512" \
+            -s "ssl_tls13_pick_key_cert:selected signature algorithm rsa_pss_rsae_sha512"
+
+requires_gnutls_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check signature algorithm order, G->m" \
+            "$P_SRV debug_level=4 force_version=tls13 auth_mode=required
+                    crt_file2=data_files/server2-sha256.crt key_file2=data_files/server2.key
+                    crt_file=data_files/server5.crt key_file=data_files/server5.key
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256 " \
+            "$G_NEXT_CLI_NO_CERT localhost -d 4 --x509cafile data_files/test-ca_cat12.crt \
+                                 --x509certfile data_files/server2-sha256.crt --x509keyfile data_files/server2.key \
+                                 --priority=NORMAL:-SIGN-ALL:+SIGN-RSA-SHA512:+SIGN-RSA-PSS-RSAE-SHA512:+SIGN-RSA-PSS-RSAE-SHA384"  \
+            0 \
+            -c "Negotiated version: 3.4" \
+            -c "HTTP/1.0 200 [Oo][Kk]" \
+            -s "select_sig_alg_for_certificate_verify:selected signature algorithm rsa_pss_rsae_sha512" \
+            -s "ssl_tls13_pick_key_cert:selected signature algorithm rsa_pss_rsae_sha512"
+
+requires_gnutls_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+run_test    "TLS 1.3: Check server no suitable signature algorithm, G->m" \
+            "$P_SRV debug_level=4 force_version=tls13 auth_mode=required
+                    crt_file2=data_files/server2-sha256.crt key_file2=data_files/server2.key
+                    crt_file=data_files/server5.crt key_file=data_files/server5.key
+                    sig_algs=rsa_pkcs1_sha512,ecdsa_secp256r1_sha256 " \
+            "$G_NEXT_CLI_NO_CERT localhost -d 4 --x509cafile data_files/test-ca_cat12.crt \
+                                 --x509certfile data_files/server2-sha256.crt --x509keyfile data_files/server2.key \
+                                 --priority=NORMAL:-SIGN-ALL:+SIGN-RSA-SHA512:+SIGN-RSA-PSS-RSAE-SHA512:+SIGN-ECDSA-SECP521R1-SHA512"  \
+            1 \
+            -s "ssl_tls13_pick_key_cert:selected signature algorithm rsa_pss_rsae_sha512" \
+            -s "select_sig_alg_for_certificate_verify:no suitable signature algorithm found"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+run_test    "TLS 1.3: Check server no suitable signature algorithm, O->m" \
+            "$P_SRV debug_level=4 force_version=tls13 auth_mode=required
+                    crt_file2=data_files/server2-sha256.crt key_file2=data_files/server2.key
+                    crt_file=data_files/server5.crt key_file=data_files/server5.key
+                    sig_algs=rsa_pkcs1_sha512,ecdsa_secp256r1_sha256" \
+            "$O_NEXT_CLI_NO_CERT -msg -CAfile data_files/test-ca_cat12.crt \
+                                 -cert data_files/server2-sha256.crt -key data_files/server2.key \
+                                 -sigalgs rsa_pkcs1_sha512:rsa_pss_rsae_sha512:ecdsa_secp521r1_sha512"  \
+            1 \
+            -s "ssl_tls13_pick_key_cert:selected signature algorithm rsa_pss_rsae_sha512" \
+            -s "select_sig_alg_for_certificate_verify:no suitable signature algorithm found"
+
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check server no suitable signature algorithm, m->m" \
+            "$P_SRV debug_level=4 force_version=tls13 auth_mode=required
+                    crt_file2=data_files/server2-sha256.crt key_file2=data_files/server2.key
+                    crt_file=data_files/server5.crt key_file=data_files/server5.key
+                    sig_algs=rsa_pkcs1_sha512,ecdsa_secp256r1_sha256 " \
+            "$P_CLI allow_sha1=0 debug_level=4 crt_file=data_files/server2-sha256.crt key_file=data_files/server2.key \
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,ecdsa_secp521r1_sha512 \
+                    min_version=tls12 max_version=tls13 " \
+            1 \
+            -s "ssl_tls13_pick_key_cert:selected signature algorithm rsa_pss_rsae_sha512" \
+            -s "select_sig_alg_for_certificate_verify:no suitable signature algorithm found"
+
+requires_gnutls_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+run_test    "TLS 1.3: Check server no suitable certificate, G->m" \
+            "$P_SRV debug_level=4 force_version=tls13
+                    crt_file=data_files/server2-sha256.crt key_file=data_files/server2.key
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256 " \
+            "$G_NEXT_CLI_NO_CERT localhost -d 4 --x509cafile data_files/test-ca_cat12.crt \
+                                 --priority=NORMAL:-SIGN-ALL:+SIGN-ECDSA-SECP521R1-SHA512:+SIGN-ECDSA-SECP256R1-SHA256"  \
+            1 \
+            -s "ssl_tls13_pick_key_cert:no suitable certificate found"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+run_test    "TLS 1.3: Check server no suitable certificate, O->m" \
+            "$P_SRV debug_level=4 force_version=tls13
+                    crt_file=data_files/server2-sha256.crt key_file=data_files/server2.key
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256 " \
+            "$O_NEXT_CLI_NO_CERT -msg -CAfile data_files/test-ca_cat12.crt \
+                                 -sigalgs ecdsa_secp521r1_sha512:ecdsa_secp256r1_sha256"  \
+            1 \
+            -s "ssl_tls13_pick_key_cert:no suitable certificate found"
+
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check server no suitable certificate, m->m" \
+            "$P_SRV debug_level=4 force_version=tls13
+                    crt_file=data_files/server2-sha256.crt key_file=data_files/server2.key
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256 " \
+            "$P_CLI allow_sha1=0 debug_level=4 \
+                    sig_algs=ecdsa_secp521r1_sha512,ecdsa_secp256r1_sha256 \
+                    min_version=tls12 max_version=tls13 " \
+            1 \
+            -s "ssl_tls13_pick_key_cert:no suitable certificate found"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check client no signature algorithm, m->O" \
+            "$O_NEXT_SRV_NO_CERT -cert data_files/server2-sha256.crt -key data_files/server2.key
+                                 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache
+                                 -Verify 10 -sigalgs rsa_pkcs1_sha512:rsa_pss_rsae_sha512:rsa_pss_rsae_sha384:ecdsa_secp521r1_sha512" \
+            "$P_CLI debug_level=4 crt_file=data_files/server5.crt key_file=data_files/server5.key \
+                    min_version=tls12 max_version=tls13 sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256" \
+            1 \
+            -c "select_sig_alg_for_certificate_verify:no suitable signature algorithm found"
+
+requires_gnutls_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check client no signature algorithm, m->G" \
+            "$G_NEXT_SRV_NO_CERT --x509certfile data_files/server2-sha256.crt --x509keyfile data_files/server2.key
+                    -d 4
+                    --priority=NORMAL:-VERS-ALL:-SIGN-ALL:+SIGN-RSA-SHA512:+SIGN-RSA-PSS-RSAE-SHA512:+SIGN-RSA-PSS-RSAE-SHA384:+VERS-TLS1.3:+CIPHER-ALL:%NO_TICKETS " \
+            "$P_CLI debug_level=4 crt_file=data_files/server5.crt key_file=data_files/server5.key \
+                    min_version=tls12 max_version=tls13 sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256" \
+            1 \
+            -c "select_sig_alg_for_certificate_verify:no suitable signature algorithm found"
+
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_SRV_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+run_test    "TLS 1.3: Check client no signature algorithm, m->m" \
+            "$P_SRV debug_level=4 force_version=tls13 auth_mode=required
+                    crt_file2=data_files/server2-sha256.crt key_file2=data_files/server2.key
+                    crt_file=data_files/server5.crt key_file=data_files/server5.key
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp521r1_sha512" \
+            "$P_CLI debug_level=4 crt_file=data_files/server5.crt key_file=data_files/server5.key \
+                    sig_algs=rsa_pkcs1_sha512,rsa_pss_rsae_sha512,rsa_pss_rsae_sha384,ecdsa_secp256r1_sha256 \
+                    min_version=tls12 max_version=tls13 " \
+            1 \
+            -c "select_sig_alg_for_certificate_verify:no suitable signature algorithm found"
+
 # Test heap memory usage after handshake
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
 requires_config_enabled MBEDTLS_MEMORY_DEBUG