Researchers have become attracted with ternary hybrid nanoparticles because of its effectiveness in enhancing heat transfer and have gone on to further analyze the working fluid. This study is focusing on magneto-ternary nanofluid flow in a porous medium over a moving plate with Joule heating. The combination of TiO2, SiO2, and Al2O3 with water, H2O, as the based fluid is used for the analysis. Using similarity transformation, the complexity of partial differential equations (PDEs) is reduced into ordinary differential equation (ODE) systems, which are then numerically solved in MATLAB using the bvp4c function for various values of the governing parameters. The impacts of different dimensionless physical parameters on velocity, temperature as well as skin friction coefficient and local Nusselt number are reported in the form of graphs. Two solutions are achieved when the plate and free-stream are moving along mutually opposite directions. Further, local Nusselt number increases with permeability parameter and suction parameter. Also, increments in permeability parameter and the suction parameter lead to the delay in the boundary layer separation. Furthermore, by combining TiO2 with a volume percentage of SiO2-Al2O3/H2O, the heat transfer is enhanced. With an increase in nanoparticle volume fraction, the similarity solutions to exist decrease.