Due to the fascinating properties of the BAs monolayer and its promising applications, we study the structural, electronic, magnetic, and optical properties of the transition mono-doped BAs nanosheets using first-principle calculations. Two substitutional doping configurations are considered at site B (dopantB) and site As (dopantAs). The doped structure at site As is more stable than at site B for the same dopant because the difference in atomic size between the dopant and As atoms is smaller than the corresponding dopant and B atoms. We explain the magnetic moments of the doped monolayer in terms of the number of valence electrons, the oxidation number, and the coupling between the electrons in the outer shell of the dopant. The MnB, Cu, and ZnB dopings convert the semiconducting behavior of the pristine BAs monolayer into metallic behavior. The BAs monolayer becomes a dilute magnetic semiconductor under the influence of VB, Cr, FeB, CoB, and Ni dopings. Due to their half-metallic behavior, the Ti-, Mn-, Fe-, and Zn-doped BAs at the site As can be used in spintronic applications. The TiAs and MnAs doped BAs nanosheets can enhance the absorption of light in the infrared and small range of the visible light regions as compared to pristine and the other doped nanosheets. The results indicate that doped BAs monolayers can be used in various optoelectronic and spintronic applications.