Amethystea is a monospecific genus, native to temperate Asia (from Turkey to Japan). Its single species, Amethystea caerulea, is sometimes cultivated as an ornamental according to Mabberley (2008) but this is not confirmed by other sources. It is perhaps more often recorded as a weed species.
With, among others, Ajuga and Caryopteris, Amethystea belongs to Ajugoideae (Cantino & al. 1999).
Cantino P.D., Wagstaff S.J. & Olmstead R.G. (1999) Caryopteris (Lamiaceae) and the conflict between phylogenetic and pragmatic considerations in botanical nomenclature. Syst. Bot. 23: 369-386. [available online at: http://www.botany.wisc.edu/courses/botany_940/05PhyloCode/papers/Cantino&99.pdf]
Mabberley D.J. (2008) Mabberley’s plant-book (3th ed.). Cambridge University Press, Cambridge: XVIII + 1021 p.