By utilizing multimode squeezed states theory, we study the generalized nonlinear equal-power higher-power sum squeezing properties of the generalized magnetic-field component in four-state superposition multimode entangled state light field |\psi^{(4)}>q. The state is composed of multimode vacuum state, multimode coherent state and its contrary state, multimode imaginary coherent state. It is found that the state |\psi^{(4)}>q is a type of four-state superposition multimode nonclassical light field, and under certain fixed conditions, the generalized magnetic-field component in the state |\psi^{(4)}>q can display generalized nonlinear equal-power 4m-th power sum squeezing effects which change periodically.