  Motivated by spin modular representations of the symmetric groups, we propose
two generalizations of the Schur regular partitions for an odd integer $p\geq
3$. One forms a subset of the set of $p$-strict partitions, and the other forms
that of strict partitions. We prove that each set has a basic
$A^{(2)}_{p-1}$-crystal structure. For $p=3$, it reproves Schur's 1926
partition theorem, a mod 6 analog of Rogers-Ramanujan partition theorem (RRPT).
For $p=5$, it gives a computer-free proof of a conjecture by Andrews during his
3-parameter generalization of RRPT, which was first proved by
Andrews-Bessenrodt-Olsson.
