This work develops a mathematically rigorous deformation of classical p-series inspired by Ramanujan-type analytic constructions, yielding a rapidly convergent, explicitly normalizable kernel with controlled asymptotic behavior. The resulting kernel admits closed-form normalization, Mellin-type integral representations, and well-defined scaling limits, enabling its systematic use as a smooth, scale-dependent modification of Newtonian gravitational modeling while preserving the leading inverse-square structure at short distances. A detailed analysis of convergence properties, asymptotic regimes, parameter sensitivity, and stability is presented, establishing internal mathematical consistency across both local (Newtonian) and extended (galactic and cosmological) distance scales. The framework is constructed to remain analytically tractable and computationally implementable, allowing direct integration into numerical simulations and data-driven modeling pipelines. Rather than proposing a new fundamental interaction, this formulation is intended as a phenomenological, analytically controlled modeling tool that interpolates between known gravitational regimes. Its potential applicability spans precision orbital mechanics, galactic dynamics, gravitational lensing, and large-scale structure modeling, offering a unified and mathematically well-posed approach for exploring deviations from classical gravity within observationally testable bounds.