The mobile relaying technique is a critical enhancing technology in wireless communications due to a higher chance of supporting the remote user from the base station (BS) with better quality of service. This paper investigates energy-efficient (EE) mobile relaying networks, mounted on an unmanned aerial vehicle (UAV), while the unknown adversaries try to intercept the legitimate link. We aim to optimize robust transmit power both UAV and BS along, relay hovering path, speed, and acceleration. The BS sends legitimate information, which is forwarded to the user by the relay. This procedure is defined as information-causality-constraint (ICC). We jointly optimize the worst case secrecy rate (WCSR) and UAV propulsion energy consumption (PEC) for a finite time horizon. We construct the BS-UAV, the UAV-user, and the UAV-adversary channel models. We apply the UAV PEC considering UAV speed and acceleration. At last, we derive EE UAV relay-user maximization problem in the adversarial wireless networks. While the problem is non-convex, we propose an iterative and sub-optimal algorithm to optimize EE UAV relay with constraints, such as ICC, trajectory, speed, acceleration, and transmit power. First, we optimize both BS and UAV transmit power, and hovering speed for known UAV path planning and acceleration. Using the optimal transmit power and speed, we obtain the optimal trajectory and acceleration. We compare our algorithm with existing algorithms and demonstrate the improved EE UAV relaying communication for our model.