Caucasian, not used as a term of causoid race but as a term defining etnicities, is the common name of a compositian of "adygeys, abkhazians, Chechenians, Karachay-Cherkessains, Ossetians, Dahestanisans and Ingshetians" living in Caucasia. The term Circassian is also used to define Adiges. Here in Turkey erkez is the name of this etnic goup. After 1864's exile many Cicassians had to live their mother land and had to migrate. Since 1864 many Cicassians have been living in Anatolia. Ali urey, son of one of these families, have written a book about Adiges and Hittites/Hatties.
You may find many different sources on the web reviewing Circassian, Adige history. But I think you can't find urey's book in your countries. The book is written in Turkish: Ali urey, Hatti/Hititlerin Kkeni ve erkezler (The Origin of Hattis/Hittites and Circassians), iviyazısı Yayınevi, 2000.
The auther argues that Circassian and Hitit language are similar. I haven't read the book but I have read an article about the book and the auther.
Since the historians of hittite language haven't known the Adige language, they they wouldn't underline this similarity. But according the auther, today's living language of this ethnic group has very common words with Hittite language. I think this is one of the subjects to be revised by using different glasses. I think etnocentrism is one of the risks on historical researces and eurocentrism has always been dominant in historical researches. I've learned in this forum that eastern and Mesopotamian cultures had many rich historical sources. For example I liked so much to read whatever I knew, by using other friends' documents.
I wish an Adige speaking his/her mother language well shared his/her arguement with us by giving ethimological examples by comparing the Hittit and Adige language.