The influences of detuning, Kerr medium and initial atomic coherence on the atomic population and Cauchy-Schwartz inequality in the system of SU(1,1) coherent states interacting non-resonantly with a A-type three-level atom with Kerr medium are investigated. The results show that the detuning lengthens the cycle of collapse-and-reclairn of the atomic Rabi oscillation and induces steady nonclassical correlation. Kerr effects make the nonclassical correlation properties steady and shorten the cycle of collapse-and-revival of the atomic Rabi oscillation. The initial atomic coherence affects obviously on the nonclassical coherence degree between the two mode cavities, while the influence on the atomic population is not evident.