Multi-access Edge Computing (MEC) is a key technology for supporting low latency applications close to the end user. Users can access application servers in MEC instead of routing to the internet by passing through a core cellular network. Few security challenges arise as the traffic does not traverse through the core network, and these can be solved by providing authentication services in the MEC. However, authentication and application mobility issues arise in the case of multiple MECs where a user is mobile and needs continuous service from application servers, without needing to establish a new session and providing authentication information repeatedly to every new MEC it connects with. We propose two solutions, namely TC3A (Token-based Cookie transfer 3rd-party Authentication) and TS3A (Token-based State transfer 3rd-party Authentication) for resolution of authentication and application mobility issues while achieving low latency. Experiments were conducted on a testbed which emulated the handover of a user between two MECs. The results show that TC3A and TS3A provide authentication to users at reduced latency by 4.6% and 25%, respectively, as compared to simple login method, and most importantly application service continuity.