<p>This study explores non-linear dynamics of a two two-level atoms quantum system interacting with a two-mode quantized cavity field under the influence of f-deformed centrosymmetric Kerr medium and Stark effect. The system Hamiltonian consists of intensity-dependent atom–field coupling, self- and cross-phase modulation due to Kerr nonlinearity, and Stark-induced shifts. Initially, the field modes are in coherent states, and atoms are in their ground states. For this system, quantum properties such as Von Neumann entropy, population inversion, fidelity, and Quantum Fisher information are analyzed to study entanglement dynamics and parameter sensitivity. Mandel Q parameter and Wigner function reveal non-classical photon statistics and quantum phase-space features, respectively. Entanglement of formation is also studied which quantifies the atom–field correlations. The calculated results show that Kerr nonlinearity enhances dynamical complexity and phase evolution but reduces coherence and entanglement strength. Further, Stark shift subtly changes the system by detuning energy levels. These insights aid in designing controllable quantum states for quantum information applications.</p>