  We investigate representations of the $\mathbb{Z}_2^2$-graded extension of
$osp(1|2)$ which is the spectrum generating algebra of the recently introduced
$\mathbb{Z}_2^2$-graded version of superconformal mechanics. The main result is
a classification of irreducible lowest weight modules of the
$\mathbb{Z}_2^2$-graded extension of $osp(1|2)$. This is done via introduction
of Verma modules and its maximal invariant submodule generated by singular
vectors. Explicit formula of all singular vectors are also presented.
