Hi, I was in Fethiye this summer (August 2018) and the little shop near Sultan Pastane and the photographer shop (not far from McDonalds), Bancukcu, does not sell any beads anymore since a few years.
I asked them where to go and they indicated this haberdashery shop behind the fish market. It's called Yüncü Mehmet Ali and the address is Kesikkapi Mahallesi, Okul Cad./97, Sok. n° 32 in Fethiye.
The store is full of wool, cotton, ribbons, all kind of sewing and crochet materials. They also have a large choice of beads, cords and findings but they are mainly lower quality (PVC or brass), so don't expect to find silver sterling or plated gold findings and beads. However, everything is really cheap and the ladies are very helpful. They offered me some tea while they were preparing my small bags of beads.
I didn't get a chance to go to the other shops mentioned in this forum, besides Hippie Chic which is a really nice jewellery and boho clothes shop. You just want to buy everything there! The only negative side is the pressure of the sales ladies who really stick to you and push you to buy stuff.