This paper addresses the resilient distributed filtering problem for a class of time-varying multirate systems over sensor networks subject to time-correlated fading channels. The time-correlated fading channel, whose fading coefficient is described by a dynamical process, is introduced to better capture the time-correlation property of the wireless channels. Moreover, the phenomenon of stochastic gain fluctuations is taken into account to accommodate the potential implementation errors, thereby achieving resilient filtering performance. The lifting technique is employed to cast the underlying multirate system into a general signal-rate one, and then an augmented system is formulated to account for the dynamics from both the plant and the fading coefficients. Our aim is to design a distributed filter such that certain upper bound is first guaranteed on the filtering error covariance and then minimized at each sampling instant.With the help of trace operations, the gain parameters of the desired distributed filter are obtained in terms of the solutions to two sets of recursive equations. Finally, the effectiveness of the developed filtering algorithm is verified via an illustrative example.