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FeSe offers an ideal platform to investigate the role of nematicity on the electron pairing interaction in iron-based superconductors. To reveal how the superconducting gap evolves with nematicity, we measure the thermal conductivity and specfic heat of FeSe_1−xS_x, in which the nematicity is suppressed by isoelectronic sulfur substitution and a nematic quantum critical point (NQCP) appears at x_c ≈ 0.17. In the whole nematic regime, we find two-gap behavior; one is small but highly anisotropic with deep minima or line nodes, and the other is larger and more isotropic. In stark contrast, in the tetragonal regime, the larger gap becomes strongly anisotropic, demonstrating an abrupt change of the superconducting gap structure at the NQCP. As charge fluctuations of d_xz and d_yz orbitals are fundamentally different on the each side of NQCP, our observation directly implies that the orbital dependent nature of the nematic fluctuations has a strong impact on the superconducting gap structure and hence on the pairing interaction.