  We analyze the motion of the spinning body (in the pole-dipole approximation)
in the gravitational and electromagnetic fields described by the
Mathisson-Papapetrou-Dixon-Souriau equations. First, we define a novel spin
supplementary condition for the electromagnetic interactions which generalizes
the one proposed by Ohashi-Kyrian-Semer\'ak for gravity. As a result, we get
the whole family of charged spinning particle models in the curved spacetime
with remarkably simple dynamics (momentum and velocity are parallel). Applying
the reparametrization procedure, for a specific dipole moment, we obtain
equations of motion with constant mass and gyromagnetic factor. Next, we show
that these equations follows from an effective Hamiltonian formalism,
previously interpreted as a classical model of the charged Dirac particle.
