This paper explores the integration of unmanned aerial vehicle (UAV) systems in a dual-function capacity, serving as both remote base stations and mobile edge servers for offloaded computational tasks from remote users utilising non-orthogonal multiple access (NOMA) scheme. This challenge of minimising latency is addressed by formulating a comprehensive problem that encompasses key computation and communication variables, such as user transmit power, user association, and computing resource allocation. The complexity arises from the intricate interplay between binary and continuous variables, as well as the presence of non-convex constraints. To overcome these challenges, we present an innovative alternating optimisation approach that iteratively tackles the problem. The effectiveness of the proposed solution in reducing total latency and optimising the resource allocation within the considered system model is demonstrated using simulations. Furthermore, this work sheds light on the potential of leveraging UAV systems for enhancing communication and computation performance, offering insights into practical strategies for latency-sensitive applications.