"some". Otherwise you would have to write: "Tongue twisters in some of the Caucasian languages."

The latter seems simpler and better but that would depend on the context. If you're going to include "of", I would suggest adding definite article "the": "Tongue twisters in some of the Caucasian languages". With this addition, both are grammatically correct.

There is something called 'central determiner position' and we can use only one word in this position. Any people. Some friends. Two cars. If you want to use the preposition OF, then you have to put another determiner in the central position. Any of THE people. Some of YOUR friends./Some of MY friends. Two of THE cars./Two of MY cars. To answer your question, you can say 'Tongue twisters in some of THE Caucasian languages' or 'Tongue twisters in some Caucasian languages'. I prefer the second one as it uses fewer words and carry the same meaning as the first one.