  We generalize quantum Drinfeld Hecke algebras by incorporating a 2-cocycle on
the associated finite group. We identify these algebras as specializations of
deformations of twisted skew group algebras, giving an explicit connection to
Hochschild cohomology. We classify these algebras for diagonal actions, as well
as for the symmetric groups with their natural representations. Our results
show that the parameter spaces for the symmetric groups in the twisted setting
is smaller than in the untwisted setting.
