Cadmium-free quantum dots (QDs) consisting of silver-indium-gallium-sulfide (AIGS) quaternary semiconductors were successfully synthesized using a metal-dithiocarbamate complex with sufficiently high reactivity to produce metal sulfides. The introduction of a gallium diethyldithiocarbamate precursor decreased the reaction temperature to produce active intermediates, which were subsequently converted into AIGS QDs at 150 °C with silver and indium acetates. Because of the low reaction temperature, AIGS QDs with a tetragonal crystal phase were produced selectively, which favorably generated band-edge emission whose full width at half-maximum is smaller than 40 nm after they were coated with gallium sulfide (GaSy) shells. The compositional indium/gallium ratio was varied by changing the mixing ratio of the precursors used for the synthesis of the AIGS core, and the band-edge photoluminescence (PL) generated from the AIGS/GaSy core/shell QDs was blue-shifted with an increase in the gallium content in the core. Consequently, a pure green emission centered at 518 nm was obtained with a PL quantum yield as high as 68%.