The Ottoman empire had a "blood tax", which involved non-islamic citizens of the Ottoman empire paying a "jizya", which was such a steep tax, that if the citizen couldn't afford would have to give up a child to slavery. This is how the Janissary cores were formed, from christian slave children. This policy decimated populations in certain regions and propelled the Ottoman empire into being the biggest slavers in Europe prior to the Trans Atlantic slave trade.

The Ottoman empire didn't necessarily have inquisitions but there were heavy restrictions and taxes on non-islamic populations and apostates of the Muslim faith were killed, even if they changed to another Islamic sect. These executions would have to/should've followed Islamic code when it comes to killing (i believe there are rules about not ruining the enemies face or mutilating the body). The Ottoman empire was a Sunni Muslim Islamic caliphate. There were even cases of regions, such as in Bulgaria, being forcibly Islamised though these cases were far and few between. Most people in the Ottoman empire became Muslim to avoid the tax. Generally while there was discrimination i wouldn't go as far to say there were inquisitions.