The name can either be from a Russian diminutive form of Anastasia or it may be from the Arabic آسية.
In the Qu’ran, it is the name of the wife of Pharoah, the women who found Moses and raised him as her own child. Unlike her evil husband, she is considered to be one of the most pious women who ever lived in Islamic tradition. The meaning and origin of the name seems to be lost.
It is currently the 104th most popular female name in France (2009) and the 472nd most popular in Quebec, Canada (2010).
It was borne by Assia Weville, the lover of English poet Ted Hughes. It is also borne by a French pop singer simply known as Assia.
Other forms of the name include:
- Asiya (Azeri)
- Asija (Bosnian)
Source
I accidentally stumbled across the name Assia about two years ago, when it appeared in a series of books my sister took out of the library. In the Spy Girl books by Carol Hedges, the main character is called Jazmin, and her mother is called Assia.