The Chesme, or Chesma iyesi, is a Turkish spirit that may take the form of a cat (or a fish, a woman, or a fairy - but it seems most well known as a cat). In this guise it lures youths to their deaths. Those spirits that belong to a well only are a variety called kuyu iyesi.
Did I find much more on this fascinating-sounding creature? So far not. I did find this jolly snippet from a children's book, Johnnykin and the Goblins (1877) in which the hero meets such a spirit:
"If I don't happen to be a girl when you speak to me," said Chesme', "you must wait, you know, till I come round to it. Come on!"
"What a beautiful large cat you are," said Johnnykin. "Is that the kind they call Persian?"
"Yes," said Chesme, very much pleased. "We are the finest cats in the world. I come from Persia. I was born in a fountain, and Chesme is the Persian word for one. All over that country and Turkey people show you fountains which are inhabited by Chesme' cats, which are only seen by moonlight, and then appear as beautiful girls, who smile all the time, and then vanish quickly into other forms, as you have seen me do. My mother's name was Empusa. She was a Greek. Ah! you ought to have seen her change!"
Since this book is Google-digitized, I'm not allowed to post images of Chesmé here, but she's delightful and you ought to see at least one of the images. Try this link. Scroll back to pages 62 and 67.
Leland, C. Godfrey. (1877). Johnnykin and the goblins. London: Macmillan & co., 62-68.