This paper proposes a robust adaptive fixed-time control for automatic landing systems (ALS) of small-scale fixed-wing UAVs exposed to wind disturbances, parametric uncertainties, and input saturation. The control structure consists of three subsystems, i.e., the guidance system, the attitude control system, and the thrust control system. Considering the landing geometry, the guidance system computes the desired Euler angles to stabilize the dynamics of altitude deviation, lateral deviation, and lateral speed. An auxiliary system is designed to compensate for the effect of input saturation in the attitude control system. The fixed-time method, the backstepping control (BSC), the fuzzy logic control (FLC), and the integral sliding mode control (ISMC) techniques are adopted to synthesize the control law. All three functional parts of the proposed ALS are equipped with a fixed-time fuzzy sliding mode disturbance observer (FSMDO). FLC computes the gains of signum functions adaptively to attenuate the chattering. Fixed-time convergence of the system errors to an arbitrary residual set is proved by comprehensive stability analysis. Finally, the comparative simulation results verify the better dynamic response and stronger robustness under the proposed ALS.