In this article, we study the problem of task selection and scheduling in unmanned aerial vehicle (UAV)-enabled multiaccess edge computing for reconnaissance (ASSUMER). Specifically, taking into account the time-varying priorities of reconnaissance tasks, we investigate how to maximize the overall reconnaissance utility by selecting an appropriate set of tasks and scheduling their execution sequence in the multiaccess edge computing server of the UAV. The ASSUMER problem is a mixed-integer nonlinear programming (MINLP) problem, which includes both integer and continuous variables and is proved to be NP-hard. To address this challenging problem, we first model the task scheduling subproblem as a single machine scheduling problem with the deterioration effect. We find out that the optimal task scheduling can be solved efficiently given any task selection variables and propose an optimal scheduling algorithm. Second, using the proposed scheduling algorithm, the ASSUMER problem is equivalent to a binary integer programming problem with respect to the task selection variable only. We prove that the objective function falls into the category of the submodular function and transform the original problem into the problem of maximizing submodular function with the energy constraint. Third, combining the proposed scheduling algorithm with submodularity, we design an effective approximation algorithm for the ASSUMER problem and prove that the algorithm has $(1 - {e^{ - 1}})/2$ bicriterion approximation guarantee. Finally, simulation results show that the proposed algorithm can improve the overall reconnaissance utility and energy efficiency compared to five benchmark algorithms.