Connate topological superconductor (TSC) combines topological surface states with nodeless superconductivity in a single material, achieving effective $p$-wave pairing without interface complication. By combining angle-resolved photoemission spectroscopy and $in$-$situ$ molecular beam epitaxy, we studied the momentum-resolved superconductivity in $beta$-$rm{Bi_2Pd}$ film. We found that the superconducting gap of topological surface state ($Delta_{TSS} sim$ 3.8 meV) is anomalously enhanced from its bulk value ($Delta_b sim$ 0.8 meV). The ratio of $2Delta_{TSS}/k_BT_c sim14.2$, is substantially larger than the BCS value. By measuring $beta$-$rm{Bi_2Pd}$ bulk single crystal as a comparison, we clearly observed the upward-shift of chemical potential in the film. In addition, a concomitant increasing of surface weight on the topological surface state was revealed by our first principle calculation, suggesting that the Dirac-fermion-mediated parity mixing may cause this anomalous superconducting enhancement. Our results establish $beta$-$rm{Bi_2Pd}$ film as a unique case of connate TSCs with a highly enhanced topological superconducting gap, which may stabilize Majorana zero modes at a higher temperature.
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