Electronic nematic phases, in which electrons in a solid spontaneously break rotational symmetry, exist in several families of unconventional superconductors. Although long-range nematic order can either compete with or enhance superconductivity, the influence of nematic fluctuations on pairing remains unresolved. Although long-range nematic order can either compete with or enhance superconductivity, the influence of nematic fluctuations on superconducting pairing mechanisms remains unresolved. However, as recently highlighted [Nature Physics, 18, 1412 (2022)], how nematicity influences superconductivity and whether nematic fluctuations can create superconductivity on their own are crucial questions in the field. One major challenge is that nematicity is often intertwined with magnetism. The FeSe_1−xS_x family of superconductors provides an opportunity to explore this concept, as it features an isolated nematic phase that can be suppressed by sulfur substitution at a quantum critical point where the nematic fluctuations are the largest. We performed scanning tunnelling spectroscopy to visualize Boguliubov quasiparticle interference patterns, from which we determined the momentum structure of the superconducting gap near the Brillouin zone Γ point of FeSe_0.81S_0.19 [Nag et al. Nature Physics 21, 89–96 (2025)]. The results reveal an anisotropic, near nodal gap with minima that are 45° rotated with respect to the Fe-Fe direction, in stark contrast to the usual isotropic gaps due to spin-mediated pairing in other tetragonal Fe-based superconductors. Instead, we find that the gap structure agrees with theoretical predictions for superconductivity mediated by nematic fluctuations.