<p>We investigate photon blockade (PB) in a two-level atom coupled to a single-mode Kerr nonlinear cavity. Kerr nonlinearity is modeled by incorporating an appropriate nonlinear function into the cavity field’s creation and annihilation operators. By applying classical driving fields to both atom and deformed cavity field, we analyze the generalized Jaynes–Cummings model in the dispersive regime. The atomic-driven system’s energy spectrum is analytically derived, and by defining a quantitative criterion for energy nonlinearity, we establish its direct relation to PB. Numerical analysis of photon statistics under both atom and cavity driving in the presence of dissipation reveals controllable PB through tuning the driving strengths and dispersive coupling. Our results demonstrate that the PB effect can be selectively realized at single-photon resonance frequencies by properly tuning the driving strengths, dispersive coupling, and the medium’s nonlinear parameter.</p>