We study properties of spacetime around regular black holes (BHs) in modified gravity, so-called regular MOG BH. The motion of the test electrically neutral and charged, and particles with magnetic dipole moment, near the regular MOG BH, considering the BH is immersed in an external, asymptotically uniform magnetic field, have also been investigated. In a study of charged particles' dynamics, we have shown that the radius of the particle's innermost stable circular orbits (ISCOs) increases with respect to increasing the parameter of MOG, while as cyclotron frequency grows the ISCO radius decreases. Effects of MOG field on synchrotron radiation by charged particles have also been studied and obtained that the existence of the MOG parameter essentially decreases the total luminosity of the radiation. Moreover, through studies of the dynamics of magnetic dipoles, we have shown that the increase of the MOG and the magnetic coupling parameters lead to an increase of the inner radius and the width of the accretion disk consisting of test magnetized particles. Finally, it is obtained that the range for values of the magnetic coupling parameter for neutron stars orbiting supermassive black holes causes their orbits to be stable.