  In this analysis, we study the dynamics of quantum oscillator fields within
the context of a position-dependent mass (PDM) system situated in an
Einstein-Maxwell space-time, incorporating a non-zero cosmological constant.
The magnetic field is aligned along the symmetry axis direction. To analyze PDM
quantum oscillator fields, we introduce a modification to the Klein-Gordon
equation by substituting the four-momentum vector $p_{\mu} \to
\Big(p_{\mu}+i\,\eta\,X_{\mu}+i\,\mathcal{F}_{\mu}\Big)$ into the Klein-Gordon
equation, where the four-vector is defibed by $X_{\mu}=(0, r, 0, 0)$,
$\mathcal{F}_{\mu}=(0, \mathcal{F}_r, 0, 0)$ with
$\mathcal{F}_r=\frac{f'(r)}{4\,f(r)}$, and $\eta$ is the mass oscillator
frequency. The radial wave equation for the relativistic modified Klein-Gordon
equation is derived and subsequently solved for two distinct cases: (i)
$f(r)=e^{\frac{1}{2}\,\alpha\,r^2}$, and (ii) $f(r)=r^{\beta}$, where $\alpha
\geq 0, \beta \geq 0$. The resultant energy levels and wave functions for
quantum oscillator fields are demonstrated to be influenced by both the
cosmological constant and the geometrical topology parameter which breaks the
degeneracy of the energy spectrum. Furthermore, we observed noteworthy
modifications in the energy levels and wave functions when compared to the
results derived in the flat space background.
