The key challenge in composite mixed matrix membrane (MMMs) synthesis is the incompatible membrane fabrication using porous support in the dry-wet phase inversion technique. The key objective of this research to synthesis thin composite ternary (amine) mixed matrix membranes on microporous support by incorporating 10 wt. % of carbon molecular sieve (CMS) and 5-15 wt. % of diethanolamine (DEA) in polyethersulfone (PES) dope solution for the separation of carbon dioxide (CO₂) from methane (CH₄). The developed membranes were evaluated for their morphological structure, thermal and mechanical stabilities, functional groups, as well as the CO₂-CH₄ separation performance at high pressure (10-30 bar). The results showed that the developed membranes have asymmetric structure, and mechanically strong at 30 bar. A new class of PES/CMS/DEA composite MMMs exhibited improved gas permeance compared to pure PES composite polymeric membrane. The permselectivty of CO₂/CH₄ enhanced from 8.15 to 16.04 at 15 wt.% of DEA at 30 bar pressure. The performance of amine composite MMMs is theoretically predicted using a modified Maxwell model. The predictions were in good agreement with experimental data after applying the optimized values with AARE % = ~ less 2 % and R² = 0.99.