This work proposes a three-velocity three-temperature three-concentration (3V-3T-3C) model to describe the momentum, energy, and mass transfer in the macro-pores, meso-pores, and micro-pores in a tridisperse porous medium (TDPM), in the attendance of magnetic field imposition. Thereafter, the system of these highly coupled equations is solved numerically to scrutinize MHD double-diffusive free convection heat transfer in a square cavity occupied by a TDPM, for the first time. Finally, features of the pertinent parameters on the flow strength as well as heat and mass transfer are disclosed through contour plots and tables. The simulation results suggest that the elimination of the magnetic field as well as increase in the double-diffusion ratio boosts up the flow strength and embellishes the heat and mass transfer, in all scales of porosity of the TDPM. It is also scrutinized that rise in the Lewis number is accompanied by small declination in the flow strength and the heat transfer and substantial elevation in the mass transfer, in all scales of porosity. Meanwhile, the consequences of the magnetic field imposition, the double-diffusion ratio, and the Lewis number are detected to be more intense in the macro-pores, as compared with the other scales of porosity of the TDPM. Additionally, it is elucidated that change in the macro-porosity is more likely to alter the heat and mass transfer performances, as compared with the meso-porosity or micro-porosity.