  In this paper, by employing the results over Kummer extensions, we give an
arithmetic characterization of pure gaps at many totally ramified places over
the quotients of Hermitian curves, including the well-studied Hermitian curves
as special cases. The cardinality of these pure gaps is explicitly
investigated. In particular, the numbers of gaps and pure gaps at a pair of
distinct places are determined precisely, which can be regarded as an extension
of the previous work by Matthews (2001) considered Hermitian curves.
Additionally, some concrete examples are provided to illustrate our results.
