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The photon is the quantum of the electromagnetic four-potential, and therefore the massless bosonic particle associated with the electromagnetic force, commonly also called the "particle of light". Use this tag for questions about the quantum-mechanical understanding of light and/or electromagnetic interactions.
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Deriving the Coulomb force equation from the idea of virtual photon exchange?
I've gone through the same thought process as you, so I suspect the question you're really trying to answer is:
"Can the formula for the electric Coulomb potential be generated as a natural consequenc …