The generation of the steady state fourth-order squeezing and squared amplitude squeezing in a micromaser by the coherent trapping approach is investigated. The results show that if two-level atoms injected into the cavity are initially in coherent state and the flight time of the atoms inside the cavity satisfies the trapping condition, the field can evolve into a coherent trapping state which exhibits steady state fourth-order squeezing and squared amplitude squeezing in the cavity as long as the flux of the atoms is moderately large.