  We study classification of interacting fermionic symmetry-protected
topological (SPT) phases with both rotation symmetry and Abelian internal
symmetries in one, two, and three dimensions. By working out this
classification, on the one hand, we demonstrate the recently proposed
correspondence principle between crystalline topological phases and those with
internal symmetries through explicit block-state constructions. We find that
for the precise correspondence to hold it is necessary to change the central
extension structure of the symmetry group by the $\mathbb{Z}_2$ fermion parity.
On the other hand, we uncover new classes of intrinsically fermionic SPT phases
that are only enabled by interactions, both in 2D and 3D with four-fold
rotation. Moreover, several new instances of Lieb-Schultz-Mattis-type theorems
for Majorana-type fermionic SPTs are obtained and we discuss their
interpretations from the perspective of bulk-boundary correspondence.
