Abstract
This paper investigates the interaction dynamics of a four-level tripod-type atomic system coupled to a q-deformed binomial field state within a Kerr-medium. The interaction model incorporates time-dependent coupling parameter and detuning parameter, providing a more adaptable framework for describing atom-field interactions. Special focus is placed on examining how the q-deformation, time-dependent coupling parameter, detuning parameter and Kerr nonlinearity affect the system's fidelity properties and linear entropy dynamics. Our results demonstrate that the effects of the considered parameters have a significant impact on atom-field entanglement and fidelity. These findings offer valuable insights into controlled quantum systems, with potential applications in quantum information processing and nonlinear quantum optics.