  In this article, we study the generalized Duffin-Kemmer-Petiau (DKP)
oscillator under the influence of quantum flux field in the topological defects
produced by a cosmic string space-time and point-like global monopole. The
generalized DKP oscillator will be investigated through a non-minimal
substitution of the momentum operator $\vec{p} \to
\left(\vec{p}+i\,M\,\omega\,\eta^0\,f(r)\,\hat{r}\right)$ in the relativistic
DKP equation. We solve this generalized DKP oscillator in a cosmic string
space-time background and obtain the energy levels and wave function of the
oscillator field using the parametric Nikiforov-Uvarov method. Afterwards, we
solve the generalized DKP-oscillator in a point-like global monopole space-time
and obtain the energy levels and wave functions following the same method. In
fact, it is shown there that the energy eigenvalues are influenced by the
topological defect of cosmic string and point-like global monopole and gets
modified compared to flat space results, and breaks the degeneracy of the
energy levels. Furthermore, we observe that the eigenvalue solutions depends on
the quantum flux field that shows the gravitational analogue of the
Aharonov-Bohm effect and also gives us a persistent currents
