This paper proposes an adaptive prescribed performance sliding mode control method to address the input saturation problem in quadrotor UAVs. An offset function is designed to ensure that the initial values of the system errors always lie within the performance envelope. A first-order system is introduced to analyze error violation and compensate for the performance bounds, thereby enhancing system stability. An anti-windup auxiliary system and a non-singular fast terminal backstepping sliding mode controller are developed to mitigate the adverse effects of input saturation. A piecewise variable rate reaching law is designed to reduce controller chattering. An RBF neural network observer is constructed to compensate online for system modeling uncertainties and external disturbances. The uniform ultimate boundedness of all state errors is rigorously proved using Lyapunov theory. Simulation results demonstrate that, compared to traditional adaptive sliding mode control and PID control, the proposed method reduces the RMSE of the desired trajectory tracking error by 18.5% and 12.9%, respectively, and decreases the IAE by 34.3% and 23.3%, respectively, validating the effectiveness and superiority of the algorithm.