The influence of the magnetic field and off- central donor impurity on the energy spectrum and wave functions of an electron in the inverted core-shell QD are calculated. On this basis, the dependence of the binding energy and the absorption coefficient of electromagnetic waves by multilayer QD with an impurity on the magnetic field induction are investigated within the approximation of the effective mass and the rectangular potential profile of the nanosystem by the matrix method using the exact electron wave functions in nanosystem without perturbations. The linear, third-order nonlinear and total optical absorption coefficients (OACs) are calculated taking into account all possible intraband quantum transitions. The combined effect of donor position, magnetic field and core size on binding energies and optical absorption coefficients is observed. The results show that these effects cause significant changes on donor binding energy and optical absorption coefficient.