  Testing gravity theories and their parameters using observations is an
important issue in relativistic astrophysics. In this context, we investigate
the motion of test particles and their harmonic oscillations in the spacetime
of non-rotating hairy black holes (BHs) in Hordeski gravity, together with
astrophysical applications of quasiperiodic oscillations (QPOs). We show
possible values of upper and lower frequencies of twin-peak QPOs which may
occur in the orbits from innermost stable circular orbits to infinity for
various values of the Horndeski parameter $q$ in relativistic precession,
warped disk models, and three different sub-models of the epicyclic resonant
model. We also study the behaviour of the QPO orbits and their position
relative to innermost stable circular orbits (ISCOs) with respect to different
values of the parameter $q$. {It is obtained that at a critical value of the
Horndeski parameter ISCO radius takes $6M$ which has been in the pure
Schwarzschild case.} Finally, we obtain mass constraints of the central BH of
microquasars GRS 1915+105 and XTE 1550-564 at the GR limit and the possible
value of the Horndeski parameter in the frame of the above-mentioned QPO
models. The analysis of orbits of twin peak QPOs with the ratio of upper and
lower frequencies 3:2, around the BHs in the frame of relativistic precession
(RP) and epicyclic resonance (ER4) QPO models have shown that the orbits locate
close to the ISCO. The distance between QPO orbits and ISCO is obtained to be
less than the error of the observations.
