diff --git a/library/ssl_tls.c b/library/ssl_tls.c
index 140b749a2..f8e7cc28d 100644
--- a/library/ssl_tls.c
+++ b/library/ssl_tls.c
@@ -4094,6 +4094,14 @@ static int ssl_preset_suiteb_ciphersuites[] = {
  *   - But if there is a good reason, do not change the order of the algorithms.
  *   - ssl_tls12_present* is for TLS 1.2 use only.
  *   - ssl_preset_* is for TLS 1.3 only or hybrid TLS 1.3/1.2 handshakes.
+ *
+ *   `rsa_pss_rsae_*` MUST BE PUT ARTER `rsa_pkcs1_*` before below compitable fixed
+ *   The compitable issue is When
+ *   - GnuTLS/OpenSSL is configured as tls12 server with rsa key
+ *   - `mebedTLS` is configured as hybrid mode.
+ *   - The order is `rsa_pss_rsae_*`, `rsa_pkcs1_*`.
+ *   GnuTLS/OpenSSL will return `rsa_pss_rsae_*` which are not supported by
+ *   TLS 1.2 in mbedTLS.
  */
 static uint16_t ssl_preset_default_sig_algs[] = {
 
@@ -4115,18 +4123,6 @@ static uint16_t ssl_preset_default_sig_algs[] = {
 #endif /* MBEDTLS_ECDSA_C && MBEDTLS_SHA384_C &&
           MBEDTLS_ECP_DP_SECP521R1_ENABLED */
 
-#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT) && defined(MBEDTLS_SHA512_C)
-    MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA512,
-#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT && MBEDTLS_SHA512_C */
-
-#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT) && defined(MBEDTLS_SHA384_C)
-    MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA384,
-#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT && MBEDTLS_SHA384_C */
-
-#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT) && defined(MBEDTLS_SHA256_C)
-    MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA256,
-#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT && MBEDTLS_SHA256_C */
-
 #if defined(MBEDTLS_RSA_C) &&  defined(MBEDTLS_SHA512_C)
     MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA512,
 #endif /* MBEDTLS_RSA_C && MBEDTLS_SHA512_C */
@@ -4139,6 +4135,18 @@ static uint16_t ssl_preset_default_sig_algs[] = {
     MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA256,
 #endif /* MBEDTLS_RSA_C && MBEDTLS_SHA256_C */
 
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT) && defined(MBEDTLS_SHA512_C)
+    MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA512,
+#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT && MBEDTLS_SHA512_C */
+
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT) && defined(MBEDTLS_SHA384_C)
+    MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA384,
+#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT && MBEDTLS_SHA384_C */
+
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT) && defined(MBEDTLS_SHA256_C)
+    MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA256,
+#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT && MBEDTLS_SHA256_C */
+
     MBEDTLS_TLS_SIG_NONE
 };
 
diff --git a/library/ssl_tls12_client.c b/library/ssl_tls12_client.c
index 25c1797cf..f516efab1 100644
--- a/library/ssl_tls12_client.c
+++ b/library/ssl_tls12_client.c
@@ -2010,6 +2010,65 @@ static int ssl_write_encrypted_pms( mbedtls_ssl_context *ssl,
 #endif /* MBEDTLS_KEY_EXCHANGE_RSA_ENABLED ||
           MBEDTLS_KEY_EXCHANGE_RSA_PSK_ENABLED */
 
+#if defined(MBEDTLS_KEY_EXCHANGE_DHE_RSA_ENABLED) ||                       \
+    defined(MBEDTLS_KEY_EXCHANGE_ECDHE_RSA_ENABLED) ||                     \
+    defined(MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED)
+static int ssl_parse_signature_algorithm( mbedtls_ssl_context *ssl,
+                                          unsigned char **p,
+                                          unsigned char *end,
+                                          mbedtls_md_type_t *md_alg,
+                                          mbedtls_pk_type_t *pk_alg )
+{
+    *md_alg = MBEDTLS_MD_NONE;
+    *pk_alg = MBEDTLS_PK_NONE;
+
+    if( (*p) + 2 > end )
+        return( MBEDTLS_ERR_SSL_DECODE_ERROR );
+
+    /*
+     * Get hash algorithm
+     */
+    if( ( *md_alg = mbedtls_ssl_md_alg_from_hash( (*p)[0] ) )
+        == MBEDTLS_MD_NONE )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 1,
+            ( "Server used unsupported HashAlgorithm %d", *(p)[0] ) );
+        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+    }
+
+    /*
+     * Get signature algorithm
+     */
+    if( ( *pk_alg = mbedtls_ssl_pk_alg_from_sig( (*p)[1] ) )
+        == MBEDTLS_PK_NONE )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 1,
+            ( "server used unsupported SignatureAlgorithm %d", (*p)[1] ) );
+        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+    }
+
+    /*
+     * Check if the signature algorithm is acceptable
+     */
+    if( !mbedtls_ssl_sig_alg_is_offered( ssl, MBEDTLS_GET_UINT16_BE( *p, 0 ) ) )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 1,
+            ( "server used HashAlgorithm %d that was not offered", *(p)[0] ) );
+        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+    }
+
+    MBEDTLS_SSL_DEBUG_MSG( 2, ( "Server used SignatureAlgorithm %d",
+                                (*p)[1] ) );
+    MBEDTLS_SSL_DEBUG_MSG( 2, ( "Server used HashAlgorithm %d",
+                                (*p)[0] ) );
+    *p += 2;
+
+    return( 0 );
+}
+#endif /* MBEDTLS_KEY_EXCHANGE_DHE_RSA_ENABLED ||
+          MBEDTLS_KEY_EXCHANGE_ECDHE_RSA_ENABLED ||
+          MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED */
+
 #if defined(MBEDTLS_KEY_EXCHANGE_ECDH_RSA_ENABLED) || \
     defined(MBEDTLS_KEY_EXCHANGE_ECDH_ECDSA_ENABLED)
 static int ssl_get_ecdh_params_from_cert( mbedtls_ssl_context *ssl )
@@ -2303,31 +2362,14 @@ start_processing:
         unsigned char *params = ssl->in_msg + mbedtls_ssl_hs_hdr_len( ssl );
         size_t params_len = p - params;
         void *rs_ctx = NULL;
-        uint16_t sig_alg;
 
         mbedtls_pk_context * peer_pk;
 
-#if !defined(MBEDTLS_SSL_KEEP_PEER_CERTIFICATE)
-        peer_pk = &ssl->handshake->peer_pubkey;
-#else /* !MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
-        if( ssl->session_negotiate->peer_cert == NULL )
-        {
-            /* Should never happen */
-            MBEDTLS_SSL_DEBUG_MSG( 1, ( "should never happen" ) );
-            return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
-        }
-        peer_pk = &ssl->session_negotiate->peer_cert->pk;
-#endif /* MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
-
         /*
          * Handle the digitally-signed structure
          */
-        MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, 2 );
-        sig_alg = MBEDTLS_GET_UINT16_BE( p, 0 );
-        if( mbedtls_ssl_tls13_get_pk_type_and_md_alg_from_sig_alg(
-                                            sig_alg, &pk_alg, &md_alg ) != 0 &&
-            ! mbedtls_ssl_sig_alg_is_offered( ssl, sig_alg ) &&
-            ! mbedtls_ssl_sig_alg_is_supported( ssl, sig_alg ) )
+        if( ssl_parse_signature_algorithm( ssl, &p, end,
+                                           &md_alg, &pk_alg ) != 0 )
         {
             MBEDTLS_SSL_DEBUG_MSG( 1,
                 ( "bad server key exchange message" ) );
@@ -2337,9 +2379,9 @@ start_processing:
                 MBEDTLS_SSL_ALERT_MSG_ILLEGAL_PARAMETER );
             return( MBEDTLS_ERR_SSL_ILLEGAL_PARAMETER );
         }
-        p += 2;
 
-        if( !mbedtls_pk_can_do( peer_pk, pk_alg ) )
+        if( pk_alg !=
+            mbedtls_ssl_get_ciphersuite_sig_pk_alg( ciphersuite_info ) )
         {
             MBEDTLS_SSL_DEBUG_MSG( 1,
                 ( "bad server key exchange message" ) );
@@ -2397,6 +2439,18 @@ start_processing:
 
         MBEDTLS_SSL_DEBUG_BUF( 3, "parameters hash", hash, hashlen );
 
+#if !defined(MBEDTLS_SSL_KEEP_PEER_CERTIFICATE)
+        peer_pk = &ssl->handshake->peer_pubkey;
+#else /* !MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
+        if( ssl->session_negotiate->peer_cert == NULL )
+        {
+            /* Should never happen */
+            MBEDTLS_SSL_DEBUG_MSG( 1, ( "should never happen" ) );
+            return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
+        }
+        peer_pk = &ssl->session_negotiate->peer_cert->pk;
+#endif /* MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
+
         /*
          * Verify signature
          */
@@ -2415,28 +2469,8 @@ start_processing:
             rs_ctx = &ssl->handshake->ecrs_ctx.pk;
 #endif
 
-#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT)
-        if( pk_alg == MBEDTLS_PK_RSASSA_PSS )
-        {
-            const mbedtls_md_info_t* md_info;
-            mbedtls_pk_rsassa_pss_options rsassa_pss_options;
-            rsassa_pss_options.mgf1_hash_id = md_alg;
-            if( ( md_info = mbedtls_md_info_from_type( md_alg ) ) == NULL )
-            {
-                return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
-            }
-            rsassa_pss_options.expected_salt_len = mbedtls_md_get_size( md_info );
-            ret = mbedtls_pk_verify_ext( pk_alg, &rsassa_pss_options,
-                                         peer_pk,
-                                         md_alg, hash, hashlen,
-                                         p, sig_len );
-        }
-        else
-#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT */
-            ret = mbedtls_pk_verify_restartable( peer_pk,
-                        md_alg, hash, hashlen, p, sig_len, rs_ctx );
-
-        if( ret != 0 )
+        if( ( ret = mbedtls_pk_verify_restartable( peer_pk,
+                        md_alg, hash, hashlen, p, sig_len, rs_ctx ) ) != 0 )
         {
 #if defined(MBEDTLS_SSL_ECP_RESTARTABLE_ENABLED)
             if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )
diff --git a/programs/ssl/ssl_test_common_source.c b/programs/ssl/ssl_test_common_source.c
index 1efbbdb5c..b720fd3b0 100644
--- a/programs/ssl/ssl_test_common_source.c
+++ b/programs/ssl/ssl_test_common_source.c
@@ -264,10 +264,14 @@ int send_cb( void *ctx, unsigned char const *buf, size_t len )
 #if defined(MBEDTLS_X509_CRT_PARSE_C)
 #if defined(MBEDTLS_ECDSA_C) && defined(MBEDTLS_RSA_C)
 #if defined(MBEDTLS_SSL_PROTO_TLS1_3)
-/* To fix version negotiation fail with RSA server key.
- * - With TLS1.3 server, `rsa_pss_rsae_*` must be sent.
- * - With TLS1.2 server, `rsa_pkcs1_*` must be sent before `rsa_pss_rsae_*`
- *   - This point is only tested with OpenSSL now.
+/*
+ *   `rsa_pss_rsae_*` MUST BE PUT ARTER `rsa_pkcs1_*` before below compitable fixed
+ *   The compitable issue is When
+ *   - GnuTLS/OpenSSL is configured as tls12 server with rsa key
+ *   - `mebedTLS` is configured as hybrid mode.
+ *   - The order is `rsa_pss_rsae_*`, `rsa_pkcs1_*`.
+ *   GnuTLS/OpenSSL will return `rsa_pss_rsae_*` which are not supported by
+ *   TLS 1.2 in mbedTLS.
  */
 #define MBEDTLS_SSL_SIG_ALG( hash ) (( hash << 8 ) | MBEDTLS_SSL_SIG_ECDSA), \
                                     (( hash << 8 ) | MBEDTLS_SSL_SIG_RSA), \