Transition metals (TMs) have been employed as efficient sources of magnetism in non-magnetic two-dimensional (2D) materials. In this work, doping with chromium (Cr) and vanadium (V) is proposed to induce feature-rich electronic and magnetic properties in a Janus Ga2SO monolayer towards spintronic applications. The Ga2SO monolayer is a 2D semiconductor material with an energy gap of 1.30 (2.12) eV obtained from PBE(HSE06)-based calculations. Considering the structural asymmetry, different vacancy and doping sites are considered. A single Ga vacancy and pair of Ga vacancies magnetize the monolayer with total magnetic moments between 0.69 and 3.13μB, where the half-metallic nature is induced by the single Ga1 vacancy (that bound to the S atom). In these cases, the magnetism is originated mainly from S and O atoms closest to the vacancy sites. Depending on the doping site, either half-metallicity or diluted magnetic semiconductor natures are obtained by doping with Cr and V atoms with total magnetic moments of 3.00 and 2.00μB, respectively. Herein, 3d TM impurities produce mainly the system magnetism. When substituting a pair of Ga atoms, TM atoms exhibit the antiparallel spin alignment to follow the Pauli exclusion principle, retaining the novel electronic characteristics induced by a single TM dopant. Except for the case of doping with a pair of V atoms, total magnetic moments of 2.00 and 1.00μB are obtained by doping with a pair or Cr atoms and Cr/V co-doping, respectively. The non-zero magnetic moment is derived from the different interactions of each TM atom with its neighboring atoms, which will also be studied by Bader charge analysis. Our results introduce new promising 2D spintronic candidates, which are made by structural modifications at Ga sites of a non-magnetic Janus Ga2SO monolayer.