  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 $\beta$ 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.
