 Solution

There is one one-particle-irreducible Feynman diagram: an internal photon joins two points of the open fermion line, with the external photon attached to that line between them. It is the upper-left panel of the figure. Route internal photon four-momentum $k$ from the incoming side to the outgoing side; the adjacent internal fermion four-momenta are $p-k$ and $p^{\prime }-k$. The symmetry factor is one.

The vertex renormalization counterterm is an additional local contribution when forming the renormalized Feynman vertex. External-leg self-energy insertions belong to the complete three-point correlation function, rather than this amputated one-particle-irreducible Feynman diagram.