If you are in Calis, Gempa and Bim are the Supermarkets, Gempa has alcohol, Bim is a bit like Lidl's cheap but not a lot of choice. Migros and Kipa (which is Tesco owned) in/near Fethiye. They are really big Supermarkets and lots of choice. There is a free bus to Kipa from Calis. Tansas is on the road between Calis and Fethiye and belongs to Migros, it's just a smaller Supermarket. For our big shop it's Kipa or Migros, for everyday stuff needed we use Gempa.
There are lots of small Markets that have everything you might need and lots are open really late, some for 24 hours, so you will never be short of anything. There are also Pork and Chicken shops in Calis, good for breakfast needs (bacon) and bbq's (chicken)