Lightweight Mg-alloys are used for the construction of Body-in-White (BIW) structures in automotive industry. However, joining of Mg-alloy with steels would be a challenge owing to distinct physical and chemical properties, besides the insolubility. In the present numerical study, the Resistance Spot Welding (RSW) of dissimilar (Mg-alloy/steel) sheets with dome-to-dome electrodes is considered and investigated on the effect of fixed and varied electrode load schedules in terms of the current density, temperature and stress fields and nugget sizes. A fully coupled 2-D axisymmetric electrothermal-mechanical model is developed, considering the elastoplastic behaviour of the sheets and temperature dependent thermophysical and electrical properties of the electrode and sheets. Also, the contact conductance model for flow of current and heat across the interfaces and the apparent heat capacity model for phase change effects are used. It is found that the current density is non-uniform during the weld-stage, and it is maximum at the tip of Mg-alloy-steel interface than the Mg-alloy-electrode interface because of high electrical resistivity of steel (three times the Mg-alloy). Also, the high temperatures in steel sheet acted as heat source to the Mg-alloy sheet and formed its nugget at the faying surface, while the steel nugget is within itself. The coupled model predicted nugget sizes are in good agreement with the experiments from the literature. Further, the continuous heating of Mg-alloy by the steel resulted in compressive residual stresses in the former and tensile residual stresses in the later, and both have decreased with varied electrode load in contrast with the fixed load.