<p>This paper addresses an inverse potential problem governed by a fractional subdiffusion problem. Specifically, we aim to identify a space-dependent potential in a Caputo time-fractional diffusion model from boundary observations. First, we establish a local Lipschitz stability estimate for the inverse potential problem, providing theoretical insight into its well-posedness under suitable assumptions on the Neumann data. In the second part, we introduce a novel reconstruction approach based on the coupled complex boundary method to numerically solve the identification problem. The core idea of this method is to reformulate the overdetermined boundary value problem as a complex-valued diffusion equation with a Robin-type boundary condition coupling the Dirichlet and Neumann data. By exploiting the imaginary part of the resulting complex solution over the domain, we construct a least-squares type cost functional and minimize it over a suitable admissible set. We prove the existence, uniqueness, stability, and convergence of the minimizer with respect to perturbations in the boundary data. Furthermore, we show the Fréchet differentiability of the cost functional, which forms the basis for a conjugate gradient algorithm designed to approximate the minimizer of the associated Tikhonov regularization functional. Finally, one-dimensional numerical experiments are presented to illustrate the accuracy, stability, and efficiency of the proposed method.</p>