The “first” Chaghatayid coin was struck in the Ili valley of the Uyghur region in 1239-40 AD. It has a fascinating history, tied to the Fatimids in Egypt and the Crusaders in Palestine.

These silver coins do not name a ruler, but they give a mint location, Almaligh, & a date, ranging from 637 to 639 in the Islamic era. This places the coins under Genghis Khan’s son Chaghatai, who inherited the Central Asian piece of his father’s empire. https://www.zeno.ru/showgallery.php?cat=10203

The design on the reverse is a Chaghatayid original creation, but the obverse is ultimately derived from a gold coin of distant Egypt, struck over a century earlier under the Fatimid ruler al-Mansur (r. 1101-1130 AD). https://en.wikipedia.org/wiki/Al-Amir_bi-Ahkam_Allah

The style, however, is different. The letters are thick and blocky, unlike the fine Fatimid calligraphy. This leads to a likely explanation for the chronological gap. The Chaghatayids were not the only ones to imitate the Fatimid coin.

The crusaders in Palestine also struck imitations, and continued long after al-Mansur’s death. Over time, their coins developed a blocky style that our Chaghatayid coin resembles. This is a more likely direct model for the Chaghatai’s coins of Almaligh.
https://www.zeno.ru/showgallery.php?cat=15173

This does not mean that there was not also a Fatimid numismatic influence in Central Asia at the time. A gold Fatimid-imitating bracteate (a thin coin-like object used in burials in Central Asia, often imitating Byzantine coins) appeared on Ebay, said to be found near Bukhara.

Note on the scare quotes around “first”: the designation of first coin of the Chaghatyid Khanate is a numismatic convention.

Earlier, anonymous copper and gold coins were minted in Central Asia between Genghis’s and Chaghatay’s deaths - perhaps better candidates for the title. Or we could give the title to a later coin minted when the Chaghatayids became fully independent. https://www.zeno.ru/showgallery.php?cat=4798

In any case, the Crusader-Fatimid style stuck. Here is a later coin, from the 1260s AD, minted at Kashgar. The mint name is just to the right of the center symbol on the obverse.

https://www.zeno.ru/showphoto.php?photo=10279