  We extend a construction of Stipsicz-Szab\'{o} of infinitely many irreducible
exotic smooth structures of some closed four-manifolds with even $b_2^+$ and
fundamental group $\mathbb{Z}/2\mathbb{Z}$. We use the double node surgery and
rational blow down constructions of Fintushel-Stern on some elliptic fibrations
equipped with a free involution. The construction is done in an equivariant
manner and the factor manifolds are distinguished by the Seiberg-Witten
invariants of their universal covers.
