In addition, deformed Kerr medium preserve the amount of the negativity of this nonclassicality feature.

Summary and conclusion {#conclusion}
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In this paper, we have studied further physical aspects of a $\Lambda$-type three-level atom interacting with a quantized two-mode radiation field in a cavity including deformed Kerr medium in the presence of the detuning parameters with and without atom-field intensity-dependent coupling regime. We have demonstrated the importance and notability of the considered nonclassicality features (which are of special interest in the quantum optics field of research) in the Introduction of this paper. In summary, using the analytical solution of the state vector of the considered bipartite (atom-field) system which has been very recently obtained by us in [@usJOSA], first, the number-phase entropic uncertainty relation and subsequently entropy squeezing (in phase component) have been evaluated, by applying the two-mode Pegg-Barnett approach. In the continuation, other nonclassical properties of the state vector of the entire system namely, Mandel parameter, Cauchy-Schwartz inequality, Two-mode and sum squeezing have been numerically examined. In each case, we individually and simultaneously studied the effects of $` `$intensity-dependent coupling$"$ (entered by $f_{i}(n_{i})$), $` `$deformed Kerr medium$"$ (by the nonlinearity function $g_{i}(n_{i})$) and $` `$detuning parameters$"$ on the nonclassicality 