In this paper, we establish the general quantum theory of the micromazer with Kerr medium. When a two-Level atom enters into the Kerr medium cavity field of a coherent state via z motion, we analyze and calculate the atomic emission probability of different regimes (thermal-atom and ultracold-atom regimes).The influence of coupling constant χ,detuning Δ and the atomic injection rate r on the atomic emission probability is discussed emphatically.