An electron? I don't know what you're getting at here. An electrostatic field is produced with strength in proportion to the charge. However, that is not the only way an electric field can exist. For instance, they can be produced by changing magnetic fields, and when these two fields interact in a way that they mutually generate one another, that's what we call an electromagnetic wave, or "photon." Photons don't mediate charge, they simply are the carrier for the information of a changing electric or magnetic field.

It seems like you have a fundamental misunderstanding of how photons are produced, or what they do. At least in DC conditions, no photons are produced at all (since there is no changing magnetic or electric field), yet there is still current.

Current is the movement of charge. Photons are irrelevant, besides being the messengers for the electric and magnetic fields, which still only applies if those fields are changing, as no information is changed otherwise, so no bozon is necessary.

What you may be thinking of is in an AC case, where current is constantly changing as the electric field wave propagates down the transmission line. This does necessitate photons. But even then, the current is still the flow of charge, and oscillates between negative and positive.