The customization of hybrid nanofluids to achieve a particular and controlled growth rate of thermal transport is done to meet the needs of applications in heating and cooling systems, aerospace and automotive industries, etc. Due to the extensive applications, the aim of the current paper is to derive a numerical solution to a wall jet flow problem through a stretching surface. To study the flow problem, authors have considered a non-Newtonian Eyring–Powell hybrid nanofluid with water and CoFe₂O₄ and TiO₂ nanoparticles. Furthermore, the impact of a magnetic field and irregular heat sink/source are studied. To comply with the applications of the wall jet flow, the authors have presented the numerical solution for two cases; with and without a magnetic field. The numerical solution is derived with a similarity transformation and MATLAB-based bvp4c solver. The value of skin friction for wall jet flow at the surface decreases by more than 50% when the magnetic field M A = 0.2 is present. The stream function value is higher for the wall jet flow without the magnetic field. The temperature of the flow rises with the dominant strength of the heat source parameters. The results of this investigation will be beneficial to various applications that utilize the applications of a wall jet, such as in car defrosters, spray paint drying for vehicles or houses, cooling structures for the CPU of high-processor laptops, sluice gate flows, and cooling jets over turbo-machinery components, etc.