diff --git a/library/ssl_tls13_server.c b/library/ssl_tls13_server.c
index a10e59b..a854080 100644
--- a/library/ssl_tls13_server.c
+++ b/library/ssl_tls13_server.c
@@ -898,6 +898,34 @@
 
 #if defined(MBEDTLS_X509_CRT_PARSE_C) && \
     defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
+
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+static psa_algorithm_t ssl_tls13_iana_sig_alg_to_psa_alg( uint16_t sig_alg )
+{
+    switch( sig_alg )
+    {
+        case MBEDTLS_TLS1_3_SIG_ECDSA_SECP256R1_SHA256:
+            return( PSA_ALG_ECDSA( PSA_ALG_SHA_256 ) );
+        case MBEDTLS_TLS1_3_SIG_ECDSA_SECP384R1_SHA384:
+            return( PSA_ALG_ECDSA( PSA_ALG_SHA_384 ) );
+        case MBEDTLS_TLS1_3_SIG_ECDSA_SECP521R1_SHA512:
+            return( PSA_ALG_ECDSA( PSA_ALG_SHA_512 ) );
+        case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA256:
+            return( PSA_ALG_RSA_PSS( PSA_ALG_SHA_256 ) );
+        case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA384:
+            return( PSA_ALG_RSA_PSS( PSA_ALG_SHA_384 ) );
+        case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA512:
+            return( PSA_ALG_RSA_PSS( PSA_ALG_SHA_512 ) );
+        case MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA256:
+        case MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA384:
+        case MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA512:
+            return( PSA_ALG_RSA_PKCS1V15_CRYPT );
+        default:
+            return( PSA_ALG_NONE );
+    }
+}
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+
 /*
  * Pick best ( private key, certificate chain ) pair based on the signature
  * algorithms supported by the client.
@@ -923,9 +951,19 @@
 
     for( ; *sig_alg != MBEDTLS_TLS1_3_SIG_NONE; sig_alg++ )
     {
+        if( !mbedtls_ssl_sig_alg_is_offered( ssl, *sig_alg ) )
+            continue;
+
+        if( !mbedtls_ssl_tls13_sig_alg_for_cert_verify_is_supported( *sig_alg ) )
+            continue;
+
         for( key_cert = key_cert_list; key_cert != NULL;
              key_cert = key_cert->next )
         {
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+            psa_algorithm_t psa_alg = PSA_ALG_NONE;
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+
             MBEDTLS_SSL_DEBUG_CRT( 3, "certificate (chain) candidate",
                                    key_cert->cert );
 
@@ -949,8 +987,18 @@
                                      "check signature algorithm %s [%04x]",
                                      mbedtls_ssl_sig_alg_to_str( *sig_alg ),
                                      *sig_alg ) );
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+            psa_alg = ssl_tls13_iana_sig_alg_to_psa_alg( *sig_alg );
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+
             if( mbedtls_ssl_tls13_check_sig_alg_cert_key_match(
-                                            *sig_alg, &key_cert->cert->pk ) )
+                                            *sig_alg, &key_cert->cert->pk )
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+                && psa_alg != PSA_ALG_NONE &&
+                mbedtls_pk_can_do_ext( &key_cert->cert->pk, psa_alg,
+                                       PSA_KEY_USAGE_SIGN_HASH ) == 1
+#endif /* MBEDTLS_USE_PSA_CRYPTO */
+                )
             {
                 ssl->handshake->key_cert = key_cert;
                 MBEDTLS_SSL_DEBUG_MSG( 3,