  One of the most important issues in relativistic astrophysics is to explain
the origin mechanisms of (ultra)high energy charged particle components of
cosmic rays. Black holes (BHs) being huge reservoirs of (gravitational) energy
can be candidates for such particle sources. The main idea of this work is to
study the effects of scalar-tensor-vector gravity (STVG) on particle
acceleration by examining charged particle dynamics and their acceleration
through the magnetic Penrose process (MPP) near magnetized Kerr-MOG BHs. First,
we study the horizon structure of the BH. Also, we study the effective
potential to gain insight into the stability of circular orbits. Our results
show that the magnetic field can extend the region of stable circular orbits,
whereas the STVG parameter reduces the {instability} of the circular orbit. The
motion of charged particles around the magnetized BH reveals various feasible
regimes of the ionized Keplerian disk behavior. Thus, from the examination of
particle trajectories we observe that at fixed values of other parameters, the
Schwarzschild BH captures the test particle; in the case of Kerr BH, the test
particle escapes to infinity or is captured by the BH, while in Kerr-MOG BH,
the test particle is trapped in some region around BH and starts orbiting it.
On investigating the MPP, we found that with increasing magnetic field, the
behavior of orbits becomes more chaotic. As a result, the particle escapes to
infinity more quickly.
