  Some microstates of the Strominger-Vafa black hole are represented by smooth
horizonless geometries called superstrata. The standard superstrata are
deformations of ${\rm AdS}_3\times S^3$, but there are also generalizations of
superstrata on the orbifold $({\rm AdS}_3\times S^3)/\mathbb{Z}_p$. In this
paper, we discuss aspects of such orbifolded superstrata. We present a CFT
perspective on the structure of orbifolded superstrata, showing that they can
be constructed in a $p$-covering space of the orbifold CFT just as the standard
superstrata. We also explicitly write down and study the geometry of the
orbifolded superstrata, focusing on the difference from the non-orbifold case,
$p=1$. We discuss further generalization of superstrata to the ones on a
fractional spectral flow of $({\rm AdS}_3\times S^3)/\mathbb{Z}_p$. This
generalization involves new fractional mode excitations of the CFT side. We
estimate the number of those generalized superstrata, and show that their
entropy is too small to account for the Strominger-Vafa entropy. We will
discuss some implications of this result, related to the typical microstates of
the black hole and the relevant supersymmetry index.
