  In this paper, We analyze a spin-zero relativistic quantum oscillator in the
presence of the Aharonov-Bohm (AB) magnetic flux in a space-time background
produced by a point-like global monopole (PGM). Afterward, we introduce a
static Coulomb-type scalar potential and subsequently with the same type of
vector potential in the quantum system. We solve the generalized Klein-Gordon
oscillator analytically for different functions (e.g. Coulomb- and Cornell-type
functions) and obtain the bound-states solutions in each case. We discuss the
effects of topological defects associated with the scalar curvature of the
space-time and the Coulomb-type external potentials on the energy profiles and
the wave function of these oscillator fields. Furthermore, we show that the
obtained energy eigenvalues depend on the magnetic quantum flux which gives
rise to the gravitational analog of the Aharonov-Bohm (AB) effect
