The current study investigates the behavior of a constricted drop engrossed in dissimilar dielectric medium, with a precise effort on the effects of the electromagnetic (E-M) field that are applied externally. The research examines a system involving a suspended drop that exhibits higher electrical conductivity compared to the contiguous liquid pool. By employing the small shape evolution approximation in the immiscible, leaky dielectric, and Newtonian fluid framework under the creeping flow condition, we analyze how E-M field affects drop shape evolution. This shape evolution depends on factors such as the magnitude and relative orientation of the E-M field, as well as thermophysical properties and the degree of confinement. The E-M field induces hydrodynamic forces due to field coupling, which alters drop shape evolution compared to scenarios involving solely an electric field. Furthermore, in the manifestation of a magnetic field, the shape reversal phenomenon is observed which is not achievable with only electric field. The flow contours behavior in inside the drop and contiguous pool are also modified by the magnetic field. Our findings suggest that combining E-M fields could provide an alternate approach for controlling, adjusting, and enrapturing drops in numerous microfluidic expedients, thereby enhancing mixing processes.