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Using first-principles calculations based on the density functional theory, the effects of atomic vacancy defect, Frenkel-type defect and transition metal <i>Z</i> (<i>Z</i> = Sc, V and Zr) doping on magnetic and electric properties of the Ti₄N₃ MXene nanosheet were investigated comprehensively. The surface Ti and subsurface N atomic vacancies are both energetically stable based on the calculated binding energy and formation energy. In addition, the former appears easier than the latter. They can both enhance the magnetism of the Ti₄N₃ nanosheet. For atom-swapped disordering, the surface Ti-N swapped disordering is unstable, and then the Frenkel-type defect will happen. In the Frenkel-type defect system, the total magnetic moment decreases due to the enhancement of indirect magnetic exchange between surface Ti atoms bridged by the N atom. A relatively high spin polarizability of approximately 70% was detected. Furthermore, the doping effects of transition metal <i>Z</i> (<i>Z</i> = Sc, V and Zr) on Ti₄N₃ nanosheet are explored. All doped systems are structurally stable and have relatively large magnetism, which is mainly induced by the directed magnetic exchange between surface <i>Z</i> and Ti atoms. Especially in the doped Ti₄N₃-Sc system, the high spin polarizability is still reserved, suggesting that this doped system can be a potential candidate for application in spintronics.