Aiming at the problem of high-precision attitude tracking control for spacecraft, this paper designs a class of prescribed-time control laws based on periodic delayed feedback theory. The control law can drive the actual spacecraft attitude to track reference signals within any prescribed time while avoiding controller singularity issues. Furthermore, building upon the designed periodic delayed sliding mode controller, this paper introduces a preset-time extended state observer to achieve online estimation of unknown disturbances and proposes a composite control law integrating both components. This composite finite-time nonsingular control law can effectively eliminate the chattering phenomenon inherent in sliding mode control. Simulation results demonstrate that the proposed controller successfully completes the spacecraft attitude tracking control task within the prescribed time and exhibits strong robustness against external disturbances.