  In this article, we try to capture the influence of deviation from standard
Kerr black hole spacetime on observed high-frequency quasi-periodic
oscillations signal. We explore the dynamics of test particles in the field of
rotating compact objects governed by the various modifications of the standard
Kerr black hole spacetime and apply the model of epicyclic oscillations of
Keplerian discs to the observed microquasars and active galactic nuclei
high-frequency quasi-periodic oscillations data. We presented a generalized
formalism for the fitting of the high-frequency quasi-periodic oscillations
models so-called epicyclic resonance and relativistic precession models, under
the assumption of stationary, axisymmetric, and asymptotically flat spacetimes.
Recently, we have used the same set of stationary, axisymmetric, and
asymptotically flat spacetimes, and estimated the restrictions of spacetime
parameters with the help of hot-spot data of three flares observed at Sgr~A* by
GRAVITY instrument \citep{Shahzadi-et-al:2022:EPJC:}. The aim of this work is
not to test a particular theoretical model or to determine and constrain its
parameters, but to map a set of well-astrophysically motivated deviations from
classical Kerr black hole spacetime and demonstrate which ones provide the best
fit for high-frequency quasi-periodic oscillations data and could be fruitful
for future exploration.
