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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 beyond Horndeski gravity and the mass of the wormhole candidates using QPOs observed in the microquasars GRO J1655-40, GRS 1915 & thorn; 105 & XTE J1550-564 and at the center of Milky Way galaxy through Monte-Carlo-Markovian-chain (MCMC) analyses.