Xinjiang
Xinjiang, also known as East Turkmenistan, is a vast province in far-western China traditionally inhabited by Turkic peoples, particularly Uyghurs. It’s largely known today for the severe repression meted out by the Chinese regime against its Muslim Turkic inhabitants.
In the first millennium CE, there was an Indo-European group of languages spoken in the region, Tocharian. It would’ve been spoken in the vicinity of the Tarim Basin (within Xinjiang) and is known from the existence of various documents written in it between the 5th and 8th centuries CE, recovered from oasis cities on the northern edge of the basin. It’s believed that the Tocharians’ ancestors would’ve been members of the Afanasievo culture of South Siberia between 3300–2500 BCE, and migrated southwards to the Tarim Basin at some point after that. It seems that Tocharian went into decline after Uyghurs started migrating to the area from what’s now Kyrgyzstan; there are numerous documents consisting of translations from one language to the other, suggesting that a period of language shift occurred over a period of time. Tocharian was probably extinct by the 10th century CE.