The development of advanced control strategies for prosthetic hands is essential for improving performance and user experience. Soft prosthetic wrists pose substantial control challenges due to their compliant structures and nonlinear dynamics. This work presents a learning-based impedance control strategy for a tendon-driven soft continuum wrist, integrated with the PRISMA HAND II prosthesis, aimed at achieving stable and adaptive joint-space control. The proposed method combines physics-based modeling using Euler-Bernoulli beam theory and the Euler-Lagrange approach with a neural network trained to estimate unmodeled nonlinearities. Simulations achieved a Root Mean Square Error (RMSE) of (Formula presented.) rad and a settling time of 3.1 s under nominal conditions. Experimental trials recorded an average RMSE of (Formula presented.) rad and confirmed the controller’s ability to recover target trajectories under unknown external forces. The method supports compliant interaction, robust motion tracking, and trajectory recovery, positioning it as a viable solution for personalized prosthetic rehabilitation. Compared to traditional controllers like Sliding Mode Controller (SMC), Model Reference Adaptive Controller (MRAC), and Model Predictive Controller (MPC), the proposed method achieved superior accuracy and stability. This hybrid approach successfully balances analytical precision with data-driven adaptability, offering a promising pathway towards intelligent control in next-generation soft prosthetic systems.