  This work explores the dynamic properties of test particles surrounding a
distorted, deformed compact object. The astrophysical motivation was to choose
such background, which could constitute a more reasonable model of a real
situation that arises in the vicinity of compact objects with the possibility
of having parameters as the extra physical degrees of freedom. This can
facilitate associating observational data with astrophysical systems. This
work's main goal is to study the dynamic regime of motion and quasi-periodic
oscillation in this background, depending on different parameters of the
system. Also, we exercise the resonant phenomena of the radial and vertical
oscillations at their observed quasi-periodic oscillations frequency ratio of
3:2.
