  Recently, it was proved that every commutative $p$-Schur ring over a group of
order $p^3$ is Schurian. In this article, we consider the Schurity problem of
non-commutative $p$-Schur rings over groups of order $p^3$. In particular, it
is given a family of non-Schurian $p$-Schur rings over groups of order $p^3$.
