Learn Turkish: Bu yemek sadece bu yöreye özgü. - This dish is exclusive to this region.

The word özgü (exclusive to / characteristic of) always requires the noun it points to be in the dative case. So yöre (region) takes the buffer -y- and the dative -e to become yöreye (to the region).

What is the difference between yöre and bölge, and could I say "bu bölgeye özgü"?

Both mean "region", but bölge is usually a larger geographic or administrative area (like the Aegean Region). Yöre refers to a more localized, culturally specific area, often used when talking about local traditions, accents, or traditional dishes. You could definitely say bu bölgeye özgü, but yöre sounds much more natural when highlighting local cuisine.

Could I use "has" or "mahsus" instead of "özgü" in this sentence?

Yes, absolutely! Bu yöreye has and bu yöreye mahsus mean the exact same thing ("exclusive to this region"). Özgü is a word of Turkic origin, while has and mahsus are borrowed from Arabic. All three are extremely common, completely interchangeable in this context, and all require the dative case.

Is it grammatically correct to end the sentence just with "özgü" without a "to be" suffix like "-dür"?