It is studied systematically that generalized nonlinear unequal-power higher-power sum squeezing properties of generalized magnetic-field component in a new kind of three state superposition multimode Schrdinger-cat state light field which is composed of multimode complex conjugation imaginary coherent state, the contrary state of multimode complex conjugation imaginary coherent state, and multimode complex conjugation coherent state, by utilizing the theory of multimode squeezed states. It is found that the state is a new type of three state superposition multimode nonclassical light field, and under certain conditions, the generalized magnetic-field component in the state can display the effects of generalized nonlinear unequal-power higher-power sum squeezing which changes periodically.