In this paper, we study the Schrödinger equation with non-central modified Kratzer potential plus a ring-shaped like potential, which is not spherically symmetric. We connect the corresponding Schrödinger equation to the Laguerre and Jacobi equations. These lead us to have some raising and lowering operators which are first order equations. We take advantage from these first order equations and discuss the supersymmetry algebra. And also we obtain the corresponding partner Hamiltonian for Kratzer potential and investigate the commutation relation for the generators algebra
