We investigate the effects of magnetic field strength over the ground state binding energy of a hydrogenic acceptor impurity confined in a CdMnTe/CdMnTe quantum well. We apply the variational method using 1s-hydrogenic wavefunction, in the framework of the single band effective mass approximation. The effect of valence band degeneracy is considered through the energy dependent effective mass. The magnetic field dependence of the barrier height is discussed. The band gap tuning in an external magnetic field for different compositions of Mn ions is achieved using an empirical formula. Spin polaronic shifts are estimated using mean field theory for different magnetic field strengths and the well sizes. We present a theoretical study of diluted magnetic semiconductors treating the local p-d exchange interaction J between the itinerant carriers and the Mn electrons within a realistic band structure. These results are compared with the other existing available literature.