Ternary and quaternary semiconductor quantum dots (QDs) are candidates for cadmium-free alternatives. Among these, semiconductors containing elements from groups 11, 13, and 16 (i.e., I–III–VI₂) are attracting increasing attention since they are direct semiconductors whose bandgap energies in the bulk state are tunable between visible and near infrared. The quaternary system of alloys consisting of silver indium sulfide (AgInS₂; bandgap energy: E_g = 1.8 eV) and silver gallium sulfide (AgGaS₂; E_g = 2.4 eV) (i.e., Ag[In_xGa_1−x]S₂ (AIGS)) enables bandgap tuning over a wide range of visible light. However, the photoluminescence (PL) quantum yield (10–20%) of AIGS QDs is significantly lower than that of AgInS₂ (60–70%). The present study investigates how to improve the PL quantum yield of AIGS QDs via surface ligand engineering. Firstly, the use of a mixture of oleic acid and oleylamine, instead of only oleylamine, as the solvent for the QD synthesis was attempted, and a threefold improvement of the PL quantum yield was achieved. Subsequently, a post-synthetic ligand exchange was performed. Although the addition of alkylphosphine, which is known as an L-type ligand, improved the PL efficiency only by 20%, the use of metal halides, which are categorized as Z-type ligands, demonstrated a twofold to threefold improvement of the PL quantum yield, with the highest value reaching 73.4%. The same procedure was applied to the band-edge emitting core/shell-like QDs that were synthesized in one batch based on our previous findings. While the as-prepared core/shell-like QDs exhibited a PL quantum yield of only 9%, the PL quantum yield increased to 49.5% after treatment with metal halides.