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