The sulfur-substituted FeSe system, FeSe1−xSx, provides a versatile platform for studying the relationship among nematicity, antiferromagnetism, and superconductivity. Here, by nuclear magnetic resonance (NMR) and resistivity measurements up to 4.73 GPa on FeSe0.91S0.09, 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=0.5GPa, two superconductivity (SC) regions separated by the QPT appear, and antiferromagnetic (AFM) phase emerges above ∼3.3GPa. From the NMR results up to 2.1 GPa, AFM fluctuations are revealed to be characterized by the stripe-type wave vector 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 ∼2.1GPa. In addition, although the AFM fluctuations correlate with Tc 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, Tc is strongly correlated with the AFM fluctuations whereas Tc weakly depends on the AFM fluctuations when nematic order is present. Our findings on FeSe0.91S0.09 were shown to be applied to the whole FeSe1−xSx system and provide an insight into the relationship between AFM fluctuations and SC in Fe-based superconductors.