Scheduling is important in Edge computing. In contrast to the Cloud, Edge resources are hardware limited and cannot support workload-driven infrastructure scaling. Hence, resource allocation and scheduling for the Edge requires a fresh perspective. Existing Edge scheduling research assumes availability of all needed resources whenever a job request is made. This paper challenges that assumption, since not all job requests from a Cloud server can be scheduled on an Edge node. Thus, guaranteeing fairness among the clients (Cloud servers offloading jobs) while accounting for priorities of the jobs becomes a critical task. This paper presents four scheduling techniques, the first is a naive first come first serve strategy and further proposes three strategies, namely a client fair, priority fair, and hybrid that accounts for the fairness of both clients and job priorities. An evaluation on a target platform under three different scenarios, namely equal, random, and Gaussian job distributions is presented. The experimental studies highlight the low overheads and the distribution of scheduled jobs on the Edge node when compared to the naive strategy. The results confirm the superior performance of the hybrid strategy and showcase the feasibility of fair schedulers for Edge computing.