The non-fatal errors expected by this function are: GNUTLS_E_INTERRUPTED, GNUTLS_E_AGAIN, as well as GNUTLS_E_GOT_APPLICATION_DATA when called on server side.
The former two interrupt the authentication procedure due to the transport layer being interrupted, and the latter because there were pending data prior to peer initiating the re-authentication. The server should read/process that data as unauthenticated and retry calling gnutls_reauth().
When this function is called under TLS1.2 or earlier or the peer didn't advertise post-handshake auth, it always fails with GNUTLS_E_INVALID_REQUEST. The verification of the received peers certificate is delegated to the session or credentials verification callbacks. A server can check whether post handshake authentication is supported by the client by checking the session flags with gnutls_session_get_flags().
Prior to calling this function in server side, the function gnutls_certificate_server_set_request() must be called setting expectations for the received certificate (request or require). If none are set this function will return with GNUTLS_E_INVALID_REQUEST.
Note that post handshake authentication is available irrespective of the initial negotiation type (PSK or certificate). In all cases however, certificate credentials must be set to the session prior to calling this function.