  Let $L_{\widehat{osp(1|2)}}(\mathcal{l},0)$ be the simple affine vertex
operator superalgebra with admissible level $\mathcal{l}$. We prove that the
category of weak $L_{\widehat{osp(1|2)}}(\mathcal{l},0)$-modules on which the
positive part of $\widehat{osp(1|2)}$ acts locally nilpotent is semisimple.
Then we prove that $\mathbb{Q}$-graded vertex operator superalgebras
$(L_{\widehat{osp(1|2)}}(\mathcal{l},0),\omega_\xi)$ with new Virasoro elements
$\omega_\xi$ are rational and the irreducible modules are exactly the
admissible modules for $\widehat{osp(1|2)}$, where $0<\xi<1$ is a rational
number. Furthermore, we determine the Zhu's algebras
$A(L_{\widehat{osp(1|2)}}(\mathcal{l},0))$ and their bimodules
$A(L(\mathcal{l},\mathcal{j}))$ for
$(L_{\widehat{osp(1|2)}}(\mathcal{l},0),\omega_\xi)$, where $\mathcal{j}$ is
the admissible weight. As an application, we calculate the fusion rules among
the irreducible ordinary modules of
$(L_{\widehat{osp(1|2)}}(\mathcal{l},0),\omega_\xi)$.
