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We study spherically symmetric magnetically charged generic singular black hole solutions of general relativity coupled to nonlinear electrodynamics. For characteristic values of the generic spacetime parameters and the parameter characterizing the ratio of the gravitational and electromagnetic forces acting on an electrically charged particle we study the circular orbits and related epicyclic motion and its frequencies. We demonstrate that the equatorial circular orbits arc forbidden in such situations, but off-equatorial circular orbits are possible. We give dependence of the stable circular orbit on the spacetime parameters and intensity of the electromagnetic interaction of the charged particles with magnetically charged black holes. We study the possible resonance phenomena of the epicyclic frequencies and the orbital frequency of the electrically charged particles in order to fit the data of the twin high-frequency quasiperiodic oscillations of x rays observed in microquasars. Moreover, the dynamics of magnetized particles around the magnetically charged generic black hole have also been explored and it is shown that as increasing magnetic charge and magnetic moment parameters, the innermost stable circular orbit (ISCO) radius decreases and disappears at some value of the magnetic moment parameter, inversely proportional to the magnetic charge of black hole. As an astrophysical application we treated the magnetar PSR J1745-2900 orbiting around Sagittarius (Sgr) A* as a magnetized particle and showed that the magnetic charge of black hole can mimic black hole spin up to a/M = 0.865694 at nu = 2, and the spin parameter can mimic the magnetic charge parameter up to q/M = 0.578575 at nu = 1, providing exactly the same value of the ISCO radius. Finally, we predict that no magnetar with the surface magnetic field of the order of 10(14-)10(15) G can follow stable orbits, but it is possible to observe ordinary neutron stars as recycled radio pulsars in the close environment of Sgr A*.