  This research focus on the investigation of relativistic quantum dynamics of
spin0 scalar particles/fields through the utilization of the Klein-Gordon (KG)
equation within the framework of an electrovacuum space-time in the presence of
an external scalar potential. Specifically, we focus on a cylindrical symmetric
Bonnor-Melvin magnetic universe with a cosmological constant, where the
magnetic field aligns along the symmetry axis direction. We derive the radial
wave equation of the KG-equation by considering a Cornell-type scalar potential
in the background of magnetic universe and successfully obtain an analytical
eigenvalue solution for spin-0 quantum system. Notably, our findings reveal
that both the energy spectrum and the corresponding radial wave function are
significantly influenced by the presence of the cosmological constant, the
topology parameter of the space-time geometry, which induces a deficit in the
angular coordinates, and the potential parameters.
