The primary objective is to perform a numerical synthesis of a Williamson fluid that has nanoparticles added to it and is directed toward a vertical cone in a uniform transverse magnetic field, under heat and mass transport, suction and injection, and convective boundary conditions. For this particular fluid flow, by utilising similarity transformations, the partial differential equations are transformed into ordinary differential equations. Calculating these kinds of equations with their suitable bounds requires the Runge–Kutta technique in combining a shooting strategy. The functions of a vast number of parameters are graphically represented and assessed on flow field profiles. The results show the local skin friction, local Nusselt number, and local Sherwood number and the changing values of the flow constraints. Finally, the results are compared to those from the previously published works and found to be in good agreement.