Under Turkish law it is an offence to buy, sell, export or even possess genuine antiquities (which includes fossils). Exact age limits are not specified, suggesting that decisions by customs officials are subjective, though a principal measure of antiquity is rarity. At popular archeological sites like Ephesus, you may be offered “antiques” by hawkers, which are invariably fake.
In the case of carpets handled by established dealers, you run a very slight risk of investing a lot of money in a supposed “collector’s item” that turns out to be collectable only by the Turkish Republic. If you’re apprehensive about a proposed purchase, ask the dealer to prepare both a fatura (invoice) recording the exact purchase price – also necessary to satisfy customs – and a declaration stating that the item is not an antiquity. Expect a heavy fine and possibly imprisonment if you transgress these laws.