Quantum magnetotransport in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Pt</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>HgSe</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml

We present a theoretical framework to investigate quantum magnetotransport in monolayer jacutingaite, focusing on its response to external electric fields and off-resonant circularly polarized laser irradiation. Our analysis reveals a sequence of topological phase transitions triggered by tuning these external parameters. Applying a perpendicular magnetic field, we study Landau level (LL) formation, spin- and valley-polarized splitting, and magneto-optical response in distinct topological phases. We find that the zeroth LL exhibits spin- and valley-polarized splitting, leading to four distinct peaks in the DOSs for the $K$ and ${K}^{\ensuremath{'}}$ valleys. We demonstrate that reversing the electric field or flipping the light helicity changes the Dirac mass sign in specific spin-valley sectors, which in turn reverses both the Berry curvature and the magnetic moment. Our results reveal that external electric, magnetic, and off-resonant optical fields can control these conductivities. These findings highlight monolayer jacutingaite as a highly tunable platform with strong potential for future applications in photonics, optoelectronics, and topological quantum devices.