Satellite Edge Computing (SEC) is seen as a promising solution for deploying network functions in orbit to provide ubiquitous services with low latency and bandwidth to support mission-critical applications. Software Defined Networks (SDN) and Network Function Virtualization (NFV) enable SEC to manage and deploy services more flexibly. In this paper, we study a dynamic and topology-aware VNF mapping and scheduling strategy in an SDN/NVF-enabled SEC infrastructure to maximize fairness in terms of end-to-end service delay margins. We formulate the VNF mapping and scheduling problem as an Integer Nonlinear Programming problem (INLP) with the objective of minimax fairness among specified service requests taking into account the time-varying satellite network topology, traffic workload, and limited resources. We then propose the following two algorithms to solve the INLP problem: Fairness-Aware Greedy Algorithm for Dynamic VNF Mapping and Scheduling (FAGD_MASC) and Fairness-Aware Simulated Annealing-Based Algorithm for Dynamic VNF Mapping and Scheduling (FASD_MASC), which are suitable for low and high service arrival rates, respectively. Finally, we evaluate the proposed algorithms through extensive simulations. The results show that both FAGD_MASC and FASD_MASC algorithms are very close to the optimizationbased solution and outperform a benchmark solution in terms of service acceptance rate and fairness.