In this article, we develop a methodology for trajectory tracking control of a vertical takeoff and landing (VTOL) unmanned aerial vehicle (UAV) in the presence of unknown mass and time-varying external disturbances. A time-dependent shift function is introduced, which, alongside a set of barrier vector functions, enables a finite period of constrained outputs, namely, the position and velocity errors. The proposed controller also features two stable adaption laws to estimate the following: 1) the mass of the UAV and 2) a parameter relating to the bound of the external disturbances. The total closed-loop system error is shown to be uniformly ultimately bounded (UUB). This proposed strategy, which requires only the first derivative of the reference trajectory and features an implicit saturation of the thrust force, is especially apt to handle three stages of flight: vertical takeoff, constrained trajectory tracking, and landing. Simulation results are presented to validate the proposed solution. Experimental results are also included to showcase the performance of our controller in a real-world application using a quadrotor vehicle.