A method of handling authentication reject upon accessing an SNPN using credentials from a credential holder is proposed. A UE is configured with a “list of subscriber data”. The UE selects an SNPN using the configured list of subscriber data, e.g., based on the SNPN selection parameters contained in a selected entry of the list of subscriber data. Based on the selected entry, the UE selects an SNPN, and then tries to access the selected SNPN using credentials supplied by a subscribed SNPN. When UE receives an authentication reject message from the network, UE considers that the selected entry of the list of subscriber data is invalid. However, other entries related to the current selected SNPN are still valid. UE is still able to access the current selected SNPN, using credentials supplied in another entry of the list of subscriber data.