An approximate solution of the radial Schrödinger equation is obtained with a generalized group of potentials in the presence of both magnetic field and potential effect using supersymmetric quantum mechanics and shape invariance methodology. The energy bandgap of the generalized group of potentials was calculated for wave cases at the ground state. By varying the numerical values of the potential strengths, the energy band gap of Hellmann's potential and Coulomb-Hulthẻn potential respectively were obtained. It is noted that the inclusion of the potential effect greatly affects the accuracy of the results. Our calculated results are in agreement and better than the existing calculated results. The present results approximately coincide with the standard bandgap of CuZnSnS (CZTS).