Recent technological advances in electronics, sensors, and communications have accelerated the widespread deployment of Unmanned Aircraft System (UAS)-aided applications. Nevertheless, networks composed of multiple UAS and ground stations, referred to as UAS–aided communications networks, have yet to receive sufficient research attention. In this paper, we address a fundamental research challenge stunting such networks, which is how to fairly maximize the energy efficiency (throughput per energy) in networks comprising adaptive modulation-capable ground nodes. For the mobility pattern intrinsic to the UASs, we demonstrate how adaptive modulation is affected. Furthermore, we formulate the problem of maximizing fair energy efficiency as a potential game that is played between the multiple ground nodes and substantiate its stability, optimality, and convergence. Based on the formulated potential game, a data collection method is proposed to maximize the energy efficiency with a fairness constraint. Additionally, we analyze the Price of Anarchy of our proposed game–theoretic data collection method. Extensive simulations exhibit the effectiveness of our proposal under varying environments.