Sixth-generation and mobile edge computing (MEC) systems are expected to empower a wide range of applications. Unmanned aerial vehicles (UAVs) can play a vital role in improving network connectivity. Hence, our problem is to minimize the user equipment (UE) energy consumption during task offloading in a UAV assisted MEC system. To address the formulated NP-hard problem, we propose task scheduling and assignment algorithms for mapping UE tasks to fixed edge servers using UAV. Lastly, the simulation results demonstrate that the proposed algorithms yield better results than other benchmark methods in terms of total UE energy consumption. Index Terms-unmanned aerial vehicle (UAV), mobile edge computing (MEC), task scheduling, trajectory design.