Edge computing paradigms were an expedient innovation for elevating the contemporary standards of mobile and Internet networks. As specified in Multi-Access Edge Computing (MEC) standardization, edge computing serviceable infrastructures are running on virtualization technologies to provide dynamic and flexible service instances. Since the inception and operation of the services are executing at the edge level gNodeBs (gN Bs), migration of services between gN Bs is an imminent occurrence in edge computing that is contriving challenges to its feasible deployment. Security and service level latency requirements are vital parameters for such service migration operations conducted through gN B to gN B (g2g) connecting channels. In this paper, our focus is to ensure identity verification among the parties involved in a service migration through authentication and to secure the migrating content through a robust g2g channel establishment. Our proposed authentication protocol was designed in accordance with the MEC architectural standardization. We have verified the proposed protocol employing four different formal verification techniques: Scyther and AVISPA verification tools, GNY and ROR logical approaches. Further, we have developed the proposed protocol in a test-bed environment emulating the MEC system with an integrated 5G Core network.