Analysis of information sources in references of the Wikipedia article "Suku Kayı" in Indonesian language version.
That they hailed from the Kayı branch of the Oğuz confederacy seems to be a creative "rediscovery" in the genealogical concoction of the fifteenth century. It is missing not only in Ahmedi but also, and more importantly, in the Yahşi Fakih-Aşıkpaşazade narrative, which gives its own version of an elaborate genealogical family tree going back to Noah. If there was a particularly significant claim to Kayı lineage, it is hard to imagine that Yahşi Fakih would not have heard of it.
Огуз — одно из тюркских племен (кабиле), они же туркмены...Второй (род) — Кайыг/(Oghuz - one of the Turkic tribes (kabile), they are also Turkmens. Second (clan) - Kayig)