Learn Turkish: Kimisi ruhsatın kamuya ait olduğunu, kimisi özel olduğunu söylüyor. - Some say that the permit belongs to the public, some say it is private.

Because ait (belonging) and özel (private) are not verbs. To build a "that" clause like "that it belongs" or "that it is private," Turkish needs a verb root to attach the factive suffix -dık to. We use the helper verb olmak (to be) as a dummy verb for this purpose, turning the adjectives into the clauses ait olduğunu and özel olduğunu.

Why does olduğ-u-n-u end with the accusative case here?

The verb söylemek (to say/tell) takes a direct object when you are stating what is being said. The two clauses ("that the permit belongs to the public" and "that it is private") are the direct objects of söylüyor, so they must take the accusative case suffix -u.

The first clause starts with the genitive subject ruhsatın, but the second clause doesn't. Why?

Turkish naturally drops repeated subjects in parallel structures. Since ruhsatın ("the permit's") was already established in the first half, it is implied in the second. The possessive suffix -u in the second olduğu is enough to remind us that we are still talking about the permit.

What is the function of the -si suffix in kimisi?