As one would anticipate from the realization of the q-commutators by difference operators, the states of maximum localization are smeared delta functions depending on q.
Cite
@article{arxiv.q-alg/9707013,
title = {q-Uncertainty Relations},
author = {Robert J. Finkelstein},
journal= {arXiv preprint arXiv:q-alg/9707013},
year = {2009}
}