  In this paper, we study $\mathcal{P}\mathcal{R}$-anti-slant warped product
submanifold of a nearly paracosymplectic manifold $\widetilde{M}$. The
necessary and sufficient condition is obtained for the distributions allied to
the characterization of a $\mathcal{P}\mathcal{R}$-anti-slant submanifold being
integrable and totally geodesic foliation. In addition, we have defined
$\mathcal{P}\mathcal{R}$-anti-slant warped product submanifold of
$\widetilde{M}$ and gave some illustrations. Finally, we extracted the
constraints for a submanifold of $\widetilde{M}$ to be a
$\mathcal{P}\mathcal{R}$-anti-slant warped product of the form
$F\times_{f}N_{\lambda}$.
