Mobile edge computing (MEC) is widely employed to allow users to offload computation-intensive tasks due to high energy efficiency, low latency, enhanced privacy, and security .Thanks to advances in manufacturing technologies, MEC-based unmanned aerial vehicle (UAV) networks can be extensions or replacements for edge servers at ground base stations to improve the network flexibility and quality of communication. This study focuses on the non-orthogonal multiple access (NOMA) scheme, emphasizing the coexistence of near-field and far-field regions, particularly in the context of multiple UAVs integrated with edge servers. We address the challenge of the latency minimization problem by efficiently optimizing both communications and computing variables such as user association, capacity allocation, and transmit power. The designed optimization problem is a mixed integer programming problem that has extremely high complexity. To solve this problem, we propose an iterative algorithm that is designed by using block coordinate descent, convex transformation, and relaxation. Through extensive simulations, our proposed solution demonstrates effectiveness in minimizing total task offloading latency across various scenarios. The findings not only contribute a practical convex optimization method to reduce the latency in MEC systems using UAV-aided NOMA networks but also enable the operations of modern applications such as augmented reality and virtual reality on handheld user devices.