In this paper, we study the theory of four-wave mixing type noises over multicore fiber (MCF) and analyze the impacts of the noises on quantum key distribution (QKD) in the quantum and classical coexistence system. The models about four-wave mixing type noises proposed in this paper include forward inter-core four-wave mixing (FIC-FWM), backward four-wave mixing (B-FWM) and backward inter-core four-wave mixing (BIC-FWM). a) The model of FIC-FWM based on discrete change model (FIC-FWM-DCM) is proposed to obtain the precise power of FIC-FWM. Simultaneously, we further propose the model of FIC-FWM based on extended coupled-power theory (FIC-FWM-ECPT) which can obtain similar results to FIC-FWM-DCM but with lower computational complexity. b) The generation mechanism of B-FWM is proposed, and the model is built by combining forward four-wave mixing and backward Rayleigh scattering. c) The generation mechanism of BIC-FWM is proposed, and the model is built by combining FIC-FWM and B-FWM. Based on the above three models of four-wave mixing type noises, we analyze the impacts of the noises on QKD in the quantum and classical coexistence systems over MCF. The results show that the proposed models of FIC-FWM can significantly improve the simulation accuracy in the coexistence system. B-FWM noise can generate a serious impact on QKD when the guard bandwidth between quantum and classical channels is less than 250 GHz with the launch power of 2 mW. BIC-FWM noise can generate a significant impact on QKD when the frequency spacing is less than or equal to 25 GHz and the launch power is larger than 2 mW. Finally, the experiments are carried out to measure FIC-FWM, and the results show the proposed model of FIC-FWM can obtain the consistent results with experiments.