  We study non-standard Verma type modules over the Kac-Moody queer Lie
superalgebra $\mathfrak{q}(n)^{(2)}$. We give a sufficient condition under
which such modules are irreducible. We also give a classification of all
irreducible diagonal $\mathbb{Z}$-graded modules over certain Heisenberg Lie
superalgebras contained in $\mathfrak{q}(n)^{(2)}$.
