Ilknur (who is arranging the Turkish lesson groups in Calis) can offer private lessons and is very good, and not expensive.
Do you mean over and above attending school or instead of?
There is talk that non-nationals who move here and don't enroll their children in school no longer being eligible for residency here until they do - such is the concern at the numbers moving over and deciding that their children don't need schooling. This is a correct reaction - children under 16 should be in school!
Ata School in Fethiye has been excellent for our girls, they love it and I would recommend it fully.