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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 isa classification of irreducible lowest weight modules of the$\mathbb{Z}_2^2$-graded extension of $osp(1|2)$. This is done via introductionof Verma modules and its maximal invariant submodule generated by singularvectors. Explicit formula of all singular vectors are also presented.

A classification of lowest weight irreducible modules over $\mathbb{Z}_2^2$-graded extension of $osp(1|2)$