Fatigue-induced crack initiation and propagation are critical factors leading to failure in engineering structures, yet their accurate prediction remains challenging. Fatigue damage often causes unexpected failures, as the driving force for crack growth under cyclic loading can be significantly lower compared to monotonic conditions. To address this, cohesive zone modeling offers a promising approach for simulating fatigue crack growth. This study introduces a cohesive interface-based fatigue crack growth model that accounts for arbitrary quasi-static cyclic loading histories. Leveraging an established interface model that integrates damage evolution, unilateral effects, and friction \cite{sacco}, the proposed formulation incorporates subcritical damage growth and hysteretic local responses. By defining a damage measure linked to the relative displacement history at the interface, the model captures degradation of mechanical properties during alternating loading paths, including elastic phases prior to local traction reaching cohesive strength. Additionally, the interface model is extended to a multiplane framework, representing the interface response through a microstructured geometry within a representative volume element. The ultimate aim is to implement the cohesive interface model in a virtual element or finite element codes for analyzing fatigue crack nucleation and evolution in cohesive solids under cyclic loading. The model's capabilities are demonstrated through mode-I and mixed-mode simulations, with comparisons to existing numerical results from the literature \cite{choi}. Computational outcomes reveal stable and consistent fatigue crack growth, validating the proposed approach.