  In this analysis, we study the quantum motions of a non-relativistic particle
confined by the Aharonov-Bohm (AB) flux field with harmonic oscillator plus
Mie-type potential in a point-like defect. We determine the eigenvalue solution
of the particles analytically and discuss the effects of the topological defect
and flux field with this potential. This eigenvalue solution is then used in
some diatomic molecular potential models (harmonic oscillator plus Kratzer,
modified Kratzer and attractive Coulomb potentials) and presented as the
eigenvalue solutions. Afterwards, we consider a general potential form
(superposition of pseudoharmonic plus Cornell-type potential) in the quantum
system and analyse the effects of various factors on the eigenvalue solution.
It is shown that the eigenvalue solutions are modified by the topological
defect of a point-like global monopole and flux field compared to the results
obtained in the flat space
