  Based on the scalar-tensor-vector modified gravitational theory, a modified
gravity Schwarzschild black hole solution has been given in the existing
literature. Such a black hole spacetime is obtained through the inclusion of a
modified gravity coupling parameter, which corresponds to the modified
gravitational constant and the black hole charge. In this sense, the modified
gravity parameter acts as not only an enhanced gravitational effect but also a
gravitational repulsive force contribution to a test particle moving around the
black hole. Because the modified Schwarzschild spacetime is static spherical
symmetric, it is integrable. However, the spherical symmetry and the
integrability are destroyed when the black hole is immersed in an external
asymptotic uniform magnetic field and the particle is charged. Although the
magnetized modified Schwarzschild spacetime is nonintegrable and inseparable,
it allows for the application of explicit symplectic integrators when its
Hamiltonian is split into five explicitly integrable parts. Taking one of the
proposed explicit symplectic integrators and the techniques of Poincare
sections and fast Lyapunov indicators as numerical tools, we show that the
charged particle can do chaotic motions under some circumstances. Chaos is
strengthened with an increase of the modified gravity parameter from the global
phase space structures. There are similar results when the magnetic field
parameter and the particle energy increase. However, an increase of the
particle angular momentum weakens the strength of chaos.
