I copy and past for you:
Xiongnu Empire
Main article: Xiongnu
The Tarim Basin in the 3rd century CE.
Traversed by the Northern Silk Road,[16] Western Regions or Xinjiang is the Chinese name for the Tarim and Dzungaria regions of what is now northwest China. At the beginning of the Han Dynasty (206 BCE CE 220), the region was subservient to the Xiongnu, a powerful nomadic people based in modern Mongolia.
The Land was controlled by Xiongnu.
In case of Turkish don't claim Xinjiang (they could do that base on sugestion discovery should evident to claim), Mongolia could claim it be course their ancestors discovered it and controlled Xinjiang first, before Han Dynasty.