We performed molecular dynamics simulation to elucidate the adsorption behavior of hydrogen (H₂), carbon dioxide (CO₂), and methane (CH₄) on four sub-models of type II kerogens (organic matter) of varying thermal maturities over a wide range of pressures (2.75 to 20 MPa) and temperatures (323 to 423 K). The adsorption capacity was directly correlated with pressure but indirectly correlated with temperature, regardless of the kerogen or gas type. The maximum adsorption capacity was 10.6 mmol/g for the CO₂, 7.5 mmol/g for CH₄, and 3.7 mmol/g for the H₂ in overmature kerogen at 20 MPa and 323 K. In all kerogens, adsorption followed the trend CO₂ > CH₄ > H₂ attributed to the larger molecular size of CO₂, which increased its affinity toward the kerogen. In addition, the adsorption capacity was directly associated with maturity and carbon content. This behavior can be attributed to a specific functional group, i.e., H, O, N, or S, and an increase in the effective pore volume, as both are correlated with organic matter maturity, which is directly proportional to the adsorption capacity. With the increase in carbon content from 40% to 80%, the adsorption capacity increased from 2.4 to 3.0 mmol/g for H₂, 7.7 to 9.5 mmol/g for CO₂, and 4.7 to 6.3 mmol/g for CH₄ at 15 MPa and 323 K. With the increase in micropores, the porosity increased, and thus II-D offered the maximum adsorption capacity and the minimum II-A kerogen. For example, at a fixed pressure (20 MPa) and temperature (373 K), the CO₂ adsorption capacity for type II-A kerogen was 7.3 mmol/g, while type II-D adsorbed 8.9 mmol/g at the same conditions. Kerogen porosity and the respective adsorption capacities of all gases followed the order II-D > II-C > II-B > II-A, suggesting a direct correlation between the adsorption capacity and kerogen porosity. These findings thus serve as a preliminary dataset on the gas adsorption affinity of the organic-rich shale reservoirs and have potential implications for CO₂ and H₂ storage in organic-rich formations.