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Molecular understanding of the CO<sub>2</sub>-CH<sub>4</sub>-H<sub>2</sub>O mixture in clay interlayers provides crucial insights into many geochemical processes in CO<sub>2</sub>-enchanced oil/gas recovery and CO<sub>2</sub> subsurface sequestrations. In this work, we developed new molecular models by optimizing the unlike-pair Lennard-Jones (LJ) parameters for the CO<sub>2</sub>-H<sub>2</sub>O, CH<sub>4</sub>-H<sub>2</sub>O and CO<sub>2</sub>-CH<sub>4</sub> binary mixtures. The optimization utilizes the coupling parameter method in combination with Gibbs ensemble Monte Carlo (GEMC) simulations. The transferability of binary-derived parameters to ternary CO<sub>2</sub>-CH<sub>4</sub>-H<sub>2</sub>O system is further demonstrated. These optimized parameters are used to study CO<sub>2</sub>-CH<sub>4</sub>-H<sub>2</sub>O mixtures in Na-montmorillonite interlayers at 323 K and 90 bar, through grand-canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. Chemical potentials of CO<sub>2</sub>, CH<sub>4</sub>, and H<sub>2</sub>O in clay interlayer are calculated through the equation of state (EOS) with the Lennard-Jones referenced Statistical Associating Fluid Theory (SAFT-LJ), which is suitable for aqueous mixtures. The equilibrium basal spacing distances and species concentrations under different relative humidity (RH) and CO<sub>2</sub>/CH<sub>4</sub> mole fractions are determined through extensive GCMC simulations. Importantly, using the new molecular models, we find that the trend of the sorbed CO<sub>2</sub> content versus the sorbed H<sub>2</sub>O content shows good agreement with <i>in situ</i> infrared (IR) spectroscopy data by Loring et al. [<i>Environmental Science& Technology</i>, <b>2021</b>, 55, 11192-11203]. While the predicted CO<sub>2</sub> concentrations in the monolayer hydration state (1W) is higher than the experimental results due to the heterogeneous expansion of the clay mineral in experiments, the CO<sub>2</sub> content in the bilayer hydration state (2W) compares remarkably well with the experimental data. The CH<sub>4</sub> adsorption in clay interlayers is found substantially lower than that of CO<sub>2</sub>. In general, GCMC results show that water intercalation under high RH suppresses the sorption of CO<sub>2</sub> and CH<sub>4</sub>, and that Na-montmorillonite preferentially adsorbs CO<sub>2</sub> over CH<sub>4</sub>.