Methods and apparatus for using a QUIC connection established between a user equipment (UE) and a Non-3GPP InterWorking Function (N3IWF) to support untrusted non-3GPP access which facilitates Access Traffic Steering, Switching, and Splitting (ATSSS) are described. An exemplary N3IWF, implemented in accordance with features of the present invention, implements MASQUE over QUIC. In some embodiments, the Multiplexed Application Substrate over QUIC Encryption (MASQUE) over QUIC implementation as the transport for NAS. In some embodiments, QUIC connection IDs are used to delineate control plane (CP) traffic and user plane traffic being communicated over the established QUIC connection. In other embodiments, a new 3GPP Payload type header is used to delineate between control plane (CP) traffic and user plane traffic communicated over the established QUIC connection.