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Dynamics of a three-level atom in Ξ configuration interacting with two-mode cavity field in Kerr-like medium is investigated. We pay special attention to the time evolution of the occupation probabilities of atomic states in order to examine the new phenomenon i.e. the shift of atomic level occupation induced by Kerr-like medium in various initial conditions of both the cavity field and atom. Our results show that the shift effect seems independent of the initial field while varies dramatically with the initial occupation of atomic states. This observation may probe into the mechanism of the effect.