<p>This research investigates the complex gravitational dynamics of the Kepler-1625 exoplanetary system by modeling the interactions among the host star, a massive exoplanet, its candidate Neptune-sized exomoon, and a test particle within an extended restricted four-body framework. Building upon the generalized restricted four-body problem, we analytically derive and numerically locate quasi-Lagrangian points (QLPs) that extend classical equilibrium concepts to this more intricate setting. Utilizing canonical normalization and system-specific parameterization, we perform comprehensive numerical simulations encompassing trajectory tracking, spectral and resonance analyses, gravitational potential characterization, and tidal force computations. Our results identify distinct stable and unstable QLPs, reveal underlying resonance structures and chaotic behaviors, and quantify tidal stresses that potentially impact exomoon orbital evolution and internal heating. This integrative approach advances theoretical understanding and provides practical insights for future observational and mission endeavors aimed at detecting and characterizing exomoons in complex multi-body systems like Kepler-1625.</p>