  Let $F$ be a non-archimedean local field. Let $\pi_1$ and $\pi_2$ be
irreducible Arthur type representations of $\mathrm{GL}_n(F)$ and
$\mathrm{GL}_{n-1}(F)$ respectively. We study Ext branching laws when $\pi_1$
and $\pi_2$ are products of discrete series representations and their
Aubert-Zelevinsky duals. We obtain an Ext analogue of the local non-tempered
Gan-Gross-Prasad conjecture in this case.
