We have conducted a systematic study employing density functional theory (DFT) and quantum theory of atoms in molecules (QTAIM) to explore the gas sensing capabilities of nitrogen-doped single vacancy graphene quantum dots (SV/3N) decorated with transition metals (TM = Mn, Co, Cu). We have studied the interactions between TM@SV/3N and four different target gases (AsH3, NH3, PH3, and H2S) through the computation of adsorption energies, charge transfer, noncovalent interaction, density of states, band gap, and work function for 12 distinct adsorption systems. Our comprehensive analysis included an in-depth assessment of sensors' stability, sensitivity, selectivity, and reusability for practical applications. Our findings indicate that the Co@SV/3N surface strongly interacts with PH3, with the highest adsorption energy (-1.15 eV). It shows remarkable sensitivity and selectivity toward PH3, making it a promising candidate for PH3 gas sensing applications. Similarly, Mn@SV/3N exhibits high sensitivity and selectivity toward NH3, positioning it as a suitable candidate for NH3 gas sensing applications. We believe this study will provide valuable theoretical guidance for developing TM@SV/3N-based gas sensors.