Chigili.
Chinese sources from the mid-7th century, as part of the Karluk union, mention certain — zhisi, who lived between the Tashlaks and Bulats, reaching the desert areas of Dzungaria in the south. If the reconstruction of zhisi as — chigili is correct, then the chigili mentioned in medieval sources in the regions of Ili and Northern Preissykul could have been them. Perhaps later, a group of these chigili could have migrated to the Taraz area and lived in a city that might have derived its name from them — Chigili. Although the presence of a town with the same name and a population group — chigili, mentioned by Al-Muqaddasi, could have been a consequence of a part of the Proto-Qarakhanids remaining there. Their town could have been called — Chigili. The population could have been designated by this name as well, although Al-Muqaddasi's report about the presence of chigili in the Taraz area might have referred to the time of the Proto-Qarakhanids, who might have been referred to as chigili from the outside.
Mahmud Kashgari wrote in the 11th century, so he could have considered the existence of the city of Chigili in the Taraz area as a consequence of the presence of a branch of other chigili, who, as noted earlier, were settled in the Ili River area and Northern Preissykul. In trying to explain why the Oghuz referred to all Turks east of the Jaykhun as chigili, he could have expressed such an opinion. Perhaps it was based on information that at one time the Oghuz began to call all Turks east of them chigili after the name of the tribes that lived in the Taraz area.
By the way, the population of the city of Chigili might not have been a branch of ethnic chigili. Although they, like the residents of the city of Chigili, could have been called chigiltsy, similar to Taraz residents, Isfijab residents, etc., whose populations were named after the city. Therefore, Mahmud Kashgari could have considered them a branch of the actual chigili. The name of the city Chigili could have been historical, i.e., named since the time of the Proto-Qarakhanids inhabiting these places.
Moreover, ethnic chigili apparently joined the Proto-Qarakhanids (or already the Qarakhanids) later, just like the Tian Shan Karluks, "Tian Shan" Kyrgyz, Yagma, and others, which once again excludes hypotheses about the possibility of the origin of the Qarakhanid dynasty from ethnic chigili, "Tian Shan" Kyrgyz, Tian Shan Karluks, Yagma, and others.