The sulfur substituted FeSe system, FeSe$_{1-x}$S$_{x}$, provides a versatile platform for studying the relationship between nematicity, antiferromagnetism, and superconductivity. Here, by nuclear magnetic resonance (NMR) and resistivity measurements up to 4.73 GPa on FeSe$_{0.91}$S$_{0.09}$, we established the pressure($p$)-temperature($T$) phase diagram in which the nematic state is suppressed with pressure showing a nematic quantum phase transition (QPT) around $p$ = 0.5 GPa, two SC regions, separated by the QPT, appear and antiferromagnetic (AFM) phase emerges above $sim$3.3 GPa. From the NMR results up to 2.1 GPa, AFM fluctuations are revealed to be characterized by the stripe-type wavevector which remains the same for the two SC regions. Furthermore, the electronic state is found to change in character from non-Fermi liquid to Fermi liquid around the nematic QPT and persists up to $sim$ 2.1 GPa. In addition, although the AFM fluctuations correlate with $T_{rm c}$ in both SC states, demonstrating the importance of the AFM fluctuations for the appearance of SC in the system, we found that, when nematic order is absent, $T_{rm c}$ is strongly correlated with the AFM fluctuations, whereas $T_{rm c}$ weakly depends on the AFM fluctuations when nematic order is present. Our findings on FeSe$_{0.91}$S$_{0.09}$ were shown to be applied to the whole FeSe$_{1-x}$S$_{x}$ system and also provide a new insight into the relationship between AFM fluctuations and SC in Fe-based superconductors.
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