Accuracy and stability are common requirements for Quadrotor trajectory tracking systems. Designing an accurate and stable tracking controller remains challenging, particularly in unknown and dynamic environments with complex aerodynamic disturbances. We propose a Quantile-approximation-based Distributional-reinforced Uncertainty Estimator (QuaDUE) to accurately identify the effects of aerodynamic disturbances, i.e., the uncertainties between the true and estimated Control Contraction Metrics (CCMs). Taking inspiration from contraction theory and integrating the QuaDUE for uncertainties, our novel CCM-based trajectory tracking framework tracks any feasible reference trajectory precisely whilst guaranteeing exponential convergence. More importantly, the convergence and training acceleration of the distributional RL are guaranteed and analyzed, respectively, from theoretical perspectives. We also demonstrate our system under unknown and diverse aerodynamic forces. Under large aerodynamic forces (>2m/s^2), compared with the classic data-driven approach, our QuaDUE-CCM achieves at least a 56.6% improvement in tracking error. Compared with QuaDRED-MPC, a distributional RL-based approach, QuaDUE-CCM achieves at least a 3 times improvement in contraction rate.