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In this article, we try to capture the influence of deviation from standardKerr black hole spacetime on observed high-frequency quasi-periodicoscillations signal. We explore the dynamics of test particles in the field ofrotating compact objects governed by the various modifications of the standardKerr black hole spacetime and apply the model of epicyclic oscillations ofKeplerian discs to the observed microquasars and active galactic nucleihigh-frequency quasi-periodic oscillations data. We presented a generalizedformalism for the fitting of the high-frequency quasi-periodic oscillationsmodels so-called epicyclic resonance and relativistic precession models, underthe assumption of stationary, axisymmetric, and asymptotically flat spacetimes.Recently, we have used the same set of stationary, axisymmetric, andasymptotically flat spacetimes, and estimated the restrictions of spacetimeparameters with the help of hot-spot data of three flares observed at Sgr~A* byGRAVITY instrument \citep{Shahzadi-et-al:2022:EPJC:}. The aim of this work isnot to test a particular theoretical model or to determine and constrain itsparameters, but to map a set of well-astrophysically motivated deviations fromclassical Kerr black hole spacetime and demonstrate which ones provide the bestfit for high-frequency quasi-periodic oscillations data and could be fruitfulfor future exploration.

Testing alternative spacetimes by high-frequency quasi-periodic oscillations observed in microquasars and active galactic nuclei