  We quantize super Yang-Mills action in $\mathcal{N}=3$ harmonic superspace
using "Fermi-Feynman" gauge and also develop the background field formalism.
This leads to simpler propagators and Feynman rules that are useful in
performing explicit calculations. The superspace rules are used to show that
divergences do not appear at 1-loop and beyond. We also compute a finite
contribution to the effective action from a 4-point diagram at 1-loop, which
matches the expected covariant result.
