  We carry out a detailed study of the three-point fermion-photon interaction
vertex at one loop order for massive fermions in reduced quantum
electrodynamics. This calculation is carried out in arbitrary covariant gauges
and space-time dimensions within a recently proposed innovative approach based
upon an efficient combination of the first and second order formalisms of
quantum electrodynamics. This procedure provides a natural decomposition of the
vertex into its components which are longitudinal and transverse to the photon
momentum. It also separates the spin and scalar degrees of freedom of a fermion
interacting electromagnetically, allowing us to readily establish the
gauge-independence of the Pauli form factor and compute it in an expeditious
manner. All incoming and outgoing momenta are taken off-shell at the outset.
However, we present results for cases of particular kinematic interest whenever
required. For the sake of completeness, we also provide expressions for the
massive fermion self energy and photon vacuum polarization, verifying known
expressions for massless reduced quantum electrodynamics and computing the
renormalization constants ${\cal Z}_1$, ${\cal Z}_2$ and ${\cal Z}_3$. As we
provide general expressions for the computed Green functions, we readily
reproduce and confirm the results for standard quantum electrodynamics.
Comparing the two cases, we infer that the Pauli form factor for reduced
quantum electrodynamics is $8/3$ times that for the standard QED in four
dimensions, implying a higher Land\'e $g$-factor. We expect our perturbative
calculation of the fermion-photon vertex to serve as a guide for any
non-perturbative construction of this Green function, invariably required in
the Schwinger-Dyson equation studies of the subject.
