A hybrid approach integrating molecular dynamics (MD) and Grand Canonical Monte Carlo (GCMC) simulations was employed to investigate the separation efficacy of N2/CH4 across various C3N slit apertures. MD simulations enabled the determination of separation selectivity and diffusion coefficients of N2/CH4, thereby aiding in the elucidation of the separation mechanism. On the other hand, GCMC simulations provided insights into the adsorption isotherms and isosteric heats of N2 and CH4 within the C3N slit. These findings reveal that the highest selectivity of N2 over CH4 occurs at the zigzag-edge C3N with a pore size of 6.2 Å. However, this selectivity is accompanied by the smallest diffusion coefficient, attributable to size sieving effects. As the pore diameter increases, more gas molecules can permeate into the pores, leading to a rise in both the maximum adsorption capacity and the isosteric heat of methane adsorption. With increasing pressure, gas molecules tend to reach saturation at higher pressure levels. Our study primarily centers on examining the separation of N2/CH4 across various C3N slit-pores, encompassing both adsorption and diffusion phenomena. These findings offer theoretical insights and comprehension for the experimental separation of coalbed methane utilizing cheaper carbon-based materials.