absent and the resonance case is considered, the state of the system does not exhibit two-mode squeezing except in some small intervals of time. However, entering the intensity-dependent coupling leads to the two-mode squeezing in all times (the downside one). The upside plots of figures \[two-modesq\](b) (studying the effect of deformed Kerr medium) and \[two-modesq\](c) (exhibiting simultaneously the effects of deformed Kerr medium and detuning parameters) show a temporal behaviour similar to the upside plot of figure \[two-modesq\](a). From the downside plot of figure \[two-modesq\](b), it is observed that the presence of deformed Kerr medium and intensity-dependent coupling effects brings about to appear deeply two-mode squeezing. In this case, it is valuable to state that the amount of the negativity of two-mode squeezing for this situation becomes nearly $20$ times greater than the downside plot of figure \[two-modesq\](a). From the downside plot of figure \[two-modesq\](c), it seems that in the intensity-dependent coupling regime, adding the detuning parameters on the deformed Kerr medium reduces the amount of the negativity of this nonclassicality sign.\
Finally, it is deduced that intensity-dependent coupling helps clearly to occur the two-mode squeezing in $X_{1}$ and particularly the deformed Kerr medium strengthens this nonclassicality feature. Also, the 