Unmanned aerial vehicles (UAV) assisted edge computing has risen as an assuring technique to accommodate ubiquitous edge computation for resource‐limited devices. Thus, this paper proposes an approach to maximize the latency fairness in a UAV‐assisted multi‐access edge computing (MEC) system. To maximize latency fairness, the authors focus on minimizing the maximum latency experienced among the users. In here, multiple ground users (GUs) offload their tasks to MEC UAV in the absence or unavailability of ground servers due to a disaster or heavy traffic where an iterative algorithm is proposed to minimize the maximum latency among the users subject to minimum control link rate and total power constraints. Sequentially, the UAVs' 3D location, offloading ratio, GUs' transmit power and GUs' computational capacity are optimized. The location of the UAV is optimized by using the novel approach, guided pattern search algorithm while the altitude of the UAV is optimized by analyzing the elevation angle dependant behaviour of the channel gain. A simple approach is utilized for optimizing the offloading ratio of the users by considering the problem as minimizing the point‐wise maximum of two convex functions while the bisection method is used to optimize the power allocation. Numerical simulation results illustrate that the proposed approach outperforms other baseline approaches in convergence, minimizing the maximum latency and maximizing and maintaining the fairness among the GUs. Furthermore, it is proved that the guided pattern search algorithm converges at least 3.5 times better while the proposed combined optimization gives 400% fairness gain, in comparison with the baseline approach.