The Kerr-like medium is a useful way to understand the nonclassicality of light, and squeezed states can be regarded as the best nonclassical state. Thus, making use of a two-photon parametric process and a Kerr medium, the squeezed Kerr states can be generated to enhance the nonclassicality of the Kerr states. In this paper, the f-deformed photon-added squeezed Kerr states are introduced by the successive effect of the f-deformed creation operator on the squeezed Kerr states. It is observed that various types of nonclassical states can be generated by adopting appropriately the controlling parameters. Moreover, some of the nonclassical properties consisting of photon statistics, squeezing, and Husimi Q distribution function are studied numerically. It is shown that adding photons to the states enhances the nonclassical behavior. Furthermore, the operator-valued intensity-dependent function has remarkably played a crucial role in revealing the nonclassicality aspects of the system.