Silver indium sulfide (AIS)/gallium sulfide (Ga-S) core/shell QDs exhibit a narrow band-edge photoluminescence (PL) in the yellow color region, and shifting the PL wavelength is crucial for optical applications. In this study, we attempt to redshift the band-edge PL by incorporating indium sulfide (In-S) shells, which have a smaller bandgap than Ga-S and are expected to broaden the exciton wavefunction. When coated with In-S shells instead of Ga-S shells, a redshift of the band-edge PL was attained. However, an increase in defective PL and a reduction in PL quantum yield occurred due to carrier trapping associated with the extended wavefunction. To address these issues, we coated the AIS/In-S cores/shell QDs with Ga-S shells using recently developed procedures, resulting in spectrally narrow PL in the red region. Interestingly, compositional and structural analyses revealed a decrease in the In ratio, which typically leads to blue shift. The observed redshift, reaching up to 40 nm, is discussed in relation to the formation of shells with graded composition, which provide a broader wavefunction in the excited state compared to discrete shells.