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The second cohomology group (SCG) of the Jordan superalgebra$\mathcal{D}_{t}$, $t\neq 0$, is calculated by using the coefficients whichappear in the regular superbimodule $\mathrm{Reg}\mathcal{D}_t$. Contrary tothe case of algebras, this group is nontrivial thanks to the non-splittingcaused by the Wedderburn Decomposition Theorem \cite{Faber1}. First, tocalculate the SCG of a Jordan superalgebra we use split-null extension of theJordan superalgebra and the Jordan superalgebra representation. We proveconditions that satisfy the bilinear forms $h$ that determine the SCG in Jordansuperalgebras. We use these to calculate the SCG for the Jordan superalgebra$\mathcal{D}_{t}$ , $t\neq 0$. Finally, we prove that$\mathcal{H}^2(\mathcal{D}_{t},\textrm{Reg}\mathcal{D}_{t})=0\oplus\mathbb{F}^2$, $t\neq 0$.

Second cohomology group of the finite-dimensional simple Jordan superalgebra $\mathcal{D}_{t}$, $t\neq 0$