  This work presents the dynamic properties of charged test particles
influenced by the gravitational and electromagnetic fields. Accordingly, we
concentrate on the simplest static and axially symmetric metric in this work,
which contains two quadrupole parameters. One relates to the central object,
and another relates to the distortion parameter, which is linked to the
external distribution of matter. This metric may associate the observable
effects to these parameters as dynamical degrees of freedom. The astrophysical
motivation for choosing such fields is the possibility to constitute a
reasonable model for a real situation occurring in these objects' vicinity. To
test the role of large-scale magnetic fields in accretion processes, we start
by analyzing different bound orbits of timelike orbits under the influence of
the system's different parameters. In particular, studying the influence of the
strength of the magnetic field. This leads to the examine their stability
concerning radial and/or vertical oscillations. The final goal is to discuss
the oscillation modes' resonant phenomena using different resonant models for
disk-oscillation modes.
