The combination of an exact and Corner Transfer Matrix Renormalization Group (CTMRG) methods is used to study an influence of external electric and magnetic fields on existence of intriguing reentrant magnetic transitions in a coupled spin-electron model on a decorated square lattice. The two-dimensional (2D) decorated square lattice with localized nodal spins and delocalized electrons is taken into account. It was found that the competition among all involved interactions (the electron hopping, spin-spin and spin-electron interaction, external electric and magnetic fields) in combination with thermal fluctuations can produce new type of reentrant magnetic transitions. Depending on the model parameters the non-zero fields can stabilize or destabilize magnetic reentrance. In addition, an alternative and more effective way, for modulating the magnetic reentrance is found. An origin of intriguing low-temperature round maximum in the specific heat was explained as a consequence of rapid changes in the sublattice magnetizations, which is induced through a competition of all presented interactions.