the von Neumann approach, we firstly obtained the time evolution of the field entropy by which the amount of entanglement between subsystems has been determined. In addition, the position-momentum entropic uncertainty relation is evaluated, from which the entropy squeezing in position/momentum component is investigated.\
Now, due to the fact that, nonclassical states have received considerable attention in various fields of research, such as quantum optics, quantum cryptography and quantum communication [@application1; @application2; @application3], meanwhile in the continuation of our recent work in [@usJOSA] and for completing it, the main goal of the present paper is to investigate individually and simultaneously the effects of intensity-dependent coupling, deformed Kerr medium and detuning parameters on some physical properties, consist of [*number-phase entropic squeezing*]{}, [*sub-Poissonian statistics*]{}, [*Cauchy-Schwartz inequality*]{} (CSI) and two different types of [*squeezing*]{} of the state vector of the atom-field system under our consideration. As will be observed, the considered parameters in our model allow one to tune the depth and domain of the mentioned nonclassicality features (the aspects with no classical analogue) with respect to time. It is also noteworthy to declare that, as is well-known, there is a logical link between these nonclassicality features and Glauber-Sudarshan $P$-distribution function [@GSPfunction1; @GSPfunction2; 