In this paper, we have investigated a scalar particle with position-dependent mass subject to a uniform magnetic field and a quantum flux, both coming from the background which is governed by the Kaluza-Klein theory. By modifying the mass term of the scalar particle, we insert the Cornell-type potential. In the search for solutions of bound states, we determine the relativistic energy profile of the system in this background of extra dimension. Particular cases of this system are analyzed and a quantum effect can be observed: the dependence of the magnetic field on the quantum numbers of the solutions.