IIRC by varying the voltage by minute amounts (where energy supplied by W=V/C is equal to the difference between two subsequent energy states, or En-En-1), you should be able to control the maximum energy supplied to the electrons. however as this difference is very small, it is quite difficult to do so.
the greater the intensity of light, more photons are present/the incident light wave has more energy, so the current increases. voltage however is only related to how the light is produced - when an energy source is required before-hand.