FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering at ambient pressure. Here, to study how the pairing interaction evolves with nematicity, we measured the thermal conductivity and specific heat of FeSe$_{1-x}$S$_x$, where the nematicity is suppressed by isoelectronic sulfur substitution. We find that in the whole nematic ($0leq x leq 0.17$) and tetragonal ($x=0.20$) regimes, the application of small magnetic field causes a steep increase of both quantities. This indicates the existence of deep minima or line nodes in the superconducting gap function, implying that the pairing interaction is significantly anisotropic in both the nematic and the tetragonal regimes. Moreover, the present results indicate that the position of gap minima/nodes in the tetragonal regime appears to be essentially different from that in the nematic regime. These results place an important constraint on current theories.
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