Hybrid quantum systems have attracted much attention due to the fact that they combine the advantages of different physical Baby Oil subsystems.Cavity QED (cavity quantum electrodynamics) with magnons is a hybrid quantum systems that combines a YIG (Yttrium Iron Garnet) sphere and a 3D (three-dimensional) rectangular microwave cavity.Based on this hybrid photon-magnon system, we obtain an approximate analytic solution by the RWA (rotating wave approximation) with an ingenious transformation.After skillfully diagonalizing the Hamiltonian, we show that the Kerr-nonlinearity interactions could yield a negativity value of the Wigner function, periodic quadrature squeezing effects, antibunching property, and field nonclassicality in the magnon.Our work may stimulate the study of nonclassicality of photon-magnon coupling systems and Proteins its potential applications in quantum information processing.