Aman doctor

This song has been recorded with many variations, both in rural traditions and in the more urban tradition of amanes, both in Greek and Turkish.

Among its first recordings is the one by the rembetis guitarist Giorgos Katsaros, rumored to have been a friend of Al Capone, who is here seen singing it in 1995 late in his life.

He claims to have published it (‘έβγαλα’, which might imply that he created it) in 1919, though I think the first available recording by him is this one from 1928, recorded in Camden, New Jersey:

In Turkish, it seems to have been made widely disseminated and popularised through its first recording under the title Mendilim Yeşili, by New York Armenian singer Bogos Kirecciyan in 1953.
Here it is included among other versions:

It is sung on the Aegean islands, for example here by Solon Lekkas from Lesvos who performs it in the amanes style, preceded by a longer improvisation (first video below), accompanied by saz (continuously interrupted by the documentary’s unfortunate editing):

In Crete, the song takes a form which is quite similar to the Cypriot one. If I'm not mistaken (I'm no expert) the melody is here changed from the saba mode to a minor scale.

or

In Cyprus, a version of the melody is known as ‘Kotsini Trantafillia’ (Red Rose-tree). This is the song’s (almost) Cypriot variation sung by a Slovenian choir: