Khoy is 'eastern' Kurdistan for sure and it was also a homeland of the Medes. And Kurds are derived from the Medes. So people who are derived from the Medes, like Kurds, have the biggest claims to that region.
Turks can never claim these lands, because Turks are not native to Northwestern Asia anyway.
Btw, there are many different Kurdish clans and tribes in Eastern Kurdistan. One of those tribes is a
Donboli tribe. Donboli tribe of Khoy has an Ezdi origin:
The Donboli came from Bokhtan, a Kurdish region between Siirt and Cizre in what is now southeastern Turkey. The first ancestor was a certain Isa Beg, who became in 1378 the ruler of Sokmanabad. His descendant, Sheikh Ahmad Beg, entered service of the Turkmen Aq Quyunlu, and then the family held several posts in Persian administration. According to Sharafkhan Bidlisi, the members of Donboli tribes were Yezidi, but one of their leaders by the name of Isa Beg, together with other families, converted to Islam
https://en.wikipedia.org/wiki/Donboli_(tribe)