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The dynamics of charged particle in the vicinity of event horizon of a rotating charged black hole (BH) with gravitomagnetic charge from a class of vector-tensor theories of modified gravity immersed in an axially symmetric magnetic field (Bfield) has been studied. The presence of Bfield reduces the radii of innermost stable circular orbit (ISCO) of charged particle and the opposite phenomenon occurs due the parameter β which describes the deviation of modified gravity considered here from the usual Einstein-Maxwell gravity also acts to increase the radius of ISCO. Angular momentum also plays the role regarding the motion of particle which implies that larger the angular momentum easier for a particle to escape. We study the stability of orbits using Lyapunov characteristic exponent which implies more stability in the presence of Bfield. Generally, in the presence of Bfield it is easier for a particle to escape than its absence. We find twist in the trajectories of charged particles close to event horizon due to spin of BH in the presence of Bfield and there is no twist in the absence of it. Finally, we comment on possible utilization of our findings for the relativistic jets and magnetohydrodynamical out flows.