The first Türgesh Kaghan Wuzhile established the Türgesh Khaganate in 699. He had driven the Tang protégé Böri Shad. In 703 he captured Suyab and set up his authority on the territory from Chach to Turfan and Beshbaliq.
See: Klyashtorny S.G., The second Türk Empire (682–745). In: History of civilizations of Central Asia. Vol. III. The crossroads of civilizations: 250 to 750 AD. Editor: B. Litvinsky. Co-editors: Zhang Guang-da and R. Shabani Samghabadi.UNESCO publishing, 1996. – Pp. 335-347. (here: 346.)
V.A. Belyaev, S.V. Sidorovich, Tang Tallies of Credence Found at the Ak-Beshim Ancient Site. Numismatique Asiatique. A bilingual French-English review. Revue de la Société de Numismatique Asiatique n° 33, Mars 2020. p. 50.[1]
The approximate borders of Türgesh Khaganate. Wuzhile ruled over the territory from Chach to Turfan and Beshbaliq. The boundary on the south was established at the Oxus river, but Samarkand and Bukhara were lost c. 710. Khiva was part of Khwarezm. Aksu (along with the principality of Farghana) was under Western Turk rule up to 657. Above Beshbaliq, the border might be at the Altay mountain range. From there onwards, the Türgesh might control the upper Irtysh, Ob, and Tobol regions to oversee the local fur hunting business. This is supported by some archaeological sources of the early Hungarians (△), provided by Manichean (and Buddhist) symbolism, like Srostki (c. 766-780) and Zevakino (c. 9-10th century). The Turks/Türgesh (according to one opinion) might also settle some Chigils from the area of Chach in the Kama-Belaya region, who later became the Szeklers. This is also supported by some archaeological sources of the early Hungarians provided by Buddhist symbolism, like Redikor (7-9th century) and Ishimbay.
For the archaeological sources comp. Olekszij Komar: История и археология древних мадьяр в эпоху миграции. – A korai magyarság vándorlásának történeti és régészeti emlékei. [Historical and archaeological relics of the wanderings of early Hungarians] Budapest, 2018.
and

Szegedi, László: A rabanbán név magyarázata, a székely és a magyar őstörténet vázlata. [Interpretation of the term Rabanbán and the sketch of the early Hungarian and Szeker history] Előadás [lecture under publishing]: A magyarság eredete - merre mutat a nyelv, és merre a történettudomány? Magyarok X. világkongresszusa. Magyarok Világszövetsége, Budapest, 2021. aug. 17. [a tanulmánykötet előkészületben, Szerk. Sántha Attila]
Own work
Szegedi László