The Yukawa potential exhibits an exponential decay to the classical Newtonian inverse-square law, parametrised by the dimensionless coupling strength $\alpha $ and screening length $\lambda $ , providing a versatile framework for examining finite-range gravitational modifications. This study investigates the effects of Yukawa corrections on the existence and linear stability analysis of equilibrium points along with associated fractal basins of attraction in the generalized photogravitational restricted three-body problem (RTBP), incorporating a gravitational potential from a surrounding disc or belt-like structure. The analysis conducts a parallel examination of three representative celestial systems, Proxima-Centauri, Sun-Mars and Sun-Saturn systems as illustrative cases across different mass regimes. Numerical explorations indicate that the non-collinear equilibrium points exhibit a singular value for $\alpha = \alpha _{0} \approx -0.0309282 $ . Moreover, the critical mass parameter $\mu _{c}$ is found to decrease, monotonically with increasing values of $\alpha \in (-1,1)$ and $\lambda \in (0, \infty )$ , wherein progressively negative values of $\alpha $ lead to expansion of the stability domain. Additionally, the basins of attraction, which are computed through multivariate Newton-Raphson method, exhibit fractal structures that reflect the convergence properties of the iterative scheme. This investigation demonstrates that Yukawa-type modifications, significantly alter the equilibrium configurations, their stability domains and convergence properties, offering deeper understanding of gravitational interactions beyond the classical Newtonian framework.
