  We classify PBW-deformations of quadratic-constant type of certain
quantizations of exterior algebras. These correspond to the fundamental modules
of quantum $\mathfrak{sl}_N$, their duals, and their direct sums. We show that
the first two cases do not admit any deformation, while in the third case we
obtain an essentially unique algebra with good properties. We compare this
algebra with other quantum Clifford algebras appearing in the literature.
