Naturally, the first experiment for measuring the charge  of the electron by Milikan's oil drop experiment. Electrostatic attraction vs gravity- pure genius

I don't think that Millikan's oil-drop experiment quite answers the posed question as I understand it. In the oil-drop experiment the inertial and gravitational mass was supplied by the oil drop that carried the electric charge. I interpret the question as asking if there be evidence for gravity acting directly on the masses of electrons and protons themselves. I do not know the answer but wonder if particle accelerators need to allow for the downward pull of gravity on the beam path.

To the best of my knowledge the only particles that have been seen to fall are slow neutrons. Since, in the standard model, neutrons consist of quarks, which are charged, it presumably implies that charged particles fall under gravity.

On the other hand, elementary particles carrying a net charge do presumably fall, but the acceleration due to background electric fields is so much larger that it swamps the effect.

In all the above, I was referring to falling on Earth. Black holes, of course, are altogether another matter.

Thank all of you for the answers especially Jasna.

@Andrew: Milikan's experiment was an observation of falling charged oil drops in an electric field. Coulomb force versus gravitational force as an example of a small body. Oil drops are not particles in the sense of elementary particles.

It exists probably no certain proof of interactions between charge and gravity.