In this paper, an adaptive super-twisting sliding mode fault-tolerant control (FTC) method is proposed to control the attitude of a satellite with four Reaction wheels. This method has several advantages, such as preventing singularity phenomena, achieving convergence in finite time, and reducing the chattering phenomenon. Additionally, a sliding adaptive fault estimation mechanism is designed to estimate actuator faults, including complete failures, despite the influence of external disturbances and uncertainties in the satellite's attitude dynamics. Furthermore, an optimal control allocation scheme is employed to distribute the control signal to the actuators in real-time, even in the presence of faults, failures, and some limitations. To increase the accuracy of the model, the dynamics of the actuators, which have a pyramid configuration, are incorporated into the dynamics of the satellite's attitude. The stability of the closed-loop system with the proposed controller is analyzed using the Lyapunov method. Finally, the effectiveness of the proposed method is confirmed through simulations and comparisons with a traditional sliding mode method.