  In this paper, we investigate relativistic quantum dynamics of spin- $0$
massive charged particle subject to a homogeneous magnetic field in the
G\"{o}del-type space-time with potentials. We solve the Klein-Gordon equation
subject to a homogeneous magnetic field in a topologically trivial flat class
of G\"{o}del-type space-time in the presence of a Cornell-type scalar and
Coulomb-type vector potentials and analyze the effects on the energy
eigenvalues and eigenfunctions.
