We suggest an approach within the fundamental framework of variational theory to calculate the dynamics of electron-impact ionization of hydrogen and hydrogen-like ions within a magnetized quantum plasma. This model can be used to predict the magnetic field effect and the plasma shielding effect on the atomic structure and collision dynamics. As an application, the binding energies of atoms/ions in the magnetized quantum plasma environment(B∼109 G) are calculated. The electron-impact ionization processes are studied. Our results show that, compared to the inner shell, the outer shell’s binding energy is greatly affected by plasma number density and magnetic field. The present results can be used not only to test other theoretical predictions and Hamiltonian models, but also be useful for the modeling of astrophysical plasmas.