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We find an infinite family of $4D$ $\mathcal{N}=2$ interacting superconformalfield theories which enter the description of the strong-coupling limit of$SU(2N+1)$ gauge theories with hypermultiplets in the$\wedge^2(\square)+\text{Sym}^2(\square)$ . These theories arise from thecompactification of the $6D$ $(2,0)$ theory of type $A_{2N}$ on a sphere withtwo full twisted punctures and one minimal untwisted puncture. For $N=1$, thistheory is the "new" rank-1 SCFT with $\Delta(u)=3$ of Argyres and Wittig. Usingthe superconformal index, we finally pin down the properties of this theory.

A Family of $4D$ $\mathcal{N}=2$ Interacting SCFTs from the Twisted $A_{2N}$ Series