  This work investigates the motion of a non-relativistic charged particle
within the spacetime of a global monopole. We introduce the Schr\"odinger
equation to describe the particle's motion with two interactions by considering
the Kratzer and the screened modified Kratzer potential. The problem's
eigenfunctions and eigenvalues are obtained by deriving and solving the radial
equation. The effective potential encompasses both the Kratzer and
electrostatic self-interaction potential and leads to bound states solutions.
The energy spectrum is investigated, particularly emphasizing its dependence on
the system's physical parameters. The screened modified Kratzer potential and
the screened self-interaction potential reveal an important role in influencing
both the effective potential and the energy spectrum. Additionally, it also
accommodates the existence of bound states. All these behaviors are illustrated
with graphs and discussed in detail.
