There is, of course, no such thing as a massless charged particle. A massless particle travels at the speed of light relative to all inertial frames, so it cannot accelerate.
A particle with charge q in an electric field [itex]\vec E[/itex] experiences a force [itex]\vec F[/itex] = q[itex]\vec E[/itex]. The only thing that affects its acceleration is its mass. [itex]\vec F[/itex] = q[itex]\vec E[/itex] = ma. There is no other force.