  {\it Hunting} compact astrophysical objects such as black holes and
wormholes, as well as testing gravity theories, are important issues in
relativistic astrophysics. In this sense, theoretical and observational studies
of quasiperiodic oscillations (QPOs) observed in (micro)quasars become helpful
in exploring their central object, which can be a black hole or a wormhole. In
the present work, we study the throat properties of traversable wormholes
beyond Horndeski theory. Also, we investigate the circular motion of test
particles orbiting the wormhole. We analyze the test particle's effective
potential and angular momentum for circular orbits. Frequencies of radial and
vertical oscillations of the particles around stable circular orbits have also
been studied and applied in explaining the quasiperiodic oscillations mechanism
in the relativistic precession (RP) model. Finally, we obtain constraint values
for the parameters of Horndeski gravity and the mass of the wormhole candidates
using QPOs observed in the microquasars GRO J1655-40, GRS 1915+105 \& XTE
J1550-564 and at the center of Milky Way galaxy through
Monte-Carlo-Markovian-Chain (MCMC) analyses.
