This paper investigates the station-keeping control of autonomous and remotely-operated vehicles (ARVs) for free-floating manipulation under model uncertainties and external disturbances. A modified adaptive generalized super-twisting algorithm (AGSTA) enhanced by adaptive tracking differentiator (ATD) and reduced-order extended state observer (RESO) is proposed. The ATD is used to obtain the smooth reference signal and its derivative. The RESO is used to estimate and compensate for the model uncertainties and external disturbances in real-time, which enhances the robustness of the controller. The modified AGSTA ensures the fast convergence of the system states and maintains them in a predefined neighborhood of origin without overestimating control gains. Besides, the proposed new variable gain strategy completely avoids the control gains vibrating near the set minimum value. Thanks to the RESO, the proposed controller is model-free and can be easily implemented in practice. The stability of the closed-loop system is analyzed based on Lyapunov's direct method in the time domain. Finally, the proposed control scheme is applied to the station-keeping control of Haidou-1 ARV, and the simulation results confirm the superiority of the proposed control scheme over the original AGSTA.