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In this study, the Schrodinger equation (SE) with screened Kratzer potential (SKP) in the presence of external magnetic and AB-flux fields is investigated using the factorization method.The eigenvalue and eigenfunction for the system are obtained in closed form. It is found that the present of the magnetic field partially removes the degeneracy when the screening parameter of the potential was small   0.005   but the addition of the AB field removed the degeneracy faster and better. The magnetization and magnetic susceptibility of the system are evaluated at zero and finite temperatures and other thermodynamic properties of the system are discussed.More so, the presence of the AB-flux field makes the system to exhibit a both a paramagnetic and diamagnetic behavior. A straight forward extension of these results to three dimension shows that the present result is consistent with those obtained in literature.