The multiple access technique has been proposed to accommodate a number of heterogeneous communication devices to support a wide variety of applications and services in the sixth generation (6G) mobile wireless networks. Due to the inherent merits in programmability, mobility, and dynamic configuration, unmanned aerial vehicle (UAV) is admitted as the candidate technique for the 6G wireless communication networks. Moreover, UAVs are becoming the important enablers of various applications in military, surveillance, monitoring, supplies delivery, and connection recovery as a temporary hotspot, etc. However, how to efficiently integrate UAV wireless communication system with their trajectory control for 6G networks has neither been well understood nor thoroughly studied. To overcome this challenge, in this paper we propose and develop a control scheme for jointly optimizing UAV coverage probability and trajectory tracking control to efficiently support UAV communications over 6G mobile wireless networks. First, we develop a base station (BS) to UAV communication channel model, and derive the UAV's coverage probability under the Nakagami-m fading channel. Since the UAV's coverage probability depends on its relative posture (i.e., position and angle) to the BS and interfering mobile users, we then derive the UAV flying trajectory control scheme to minimize its trajectory tracking error. We also show that our proposed control schemes can attain the Lyapunov stability of trajectory error. Finally, we validate and evaluate our derived results of the UAV trajectory control scheme over 6G networks through numerical analyses.