Quadrotors are increasingly employed for both civilian and military applications. Recently, researchers have combined different control and estimation schemes to come up with a hybrid control structure to improve the robustness and tracking performance of the quadrotors. To further enhance the tracking precision of quadrotors subjected to parametric variations and environmental disturbances, this article proposes a new robust adaptive hybrid control architecture. In this study, the quadrotor model is divided into altitude, attitude, and position subsystems for which appropriate control methods are designed. A fractional-order sliding mode control with adaptive gain (AFSMC) is designed to enhance the tracking of the altitude subsystem. A robust backstepping control with adaptive gain (RAB) is developed for the horizontal position to generate the required roll and pitch orientations. A nonsingular fast terminal sliding mode control (NFTSMC) is incorporated with a finite-time disturbance observer (FDO) to accurately suppress the disturbances, follow the target rotation angles, and attain finite-time stability. The compounded control structure ensures accurate, fast, and robust tracking. The efficacy of the developed hybrid control scheme is assessed via simulations and comparisons with existing control methods.