In Antalya its a very simple procedure to obtain the check document.
First make sure you have your passport and residence permit with you, then:-
1. Head to the main Courts building (see map below)
2. Take the stairs down directly under the main entrance signposted "Sabıka kaydı" (Criminal Record)
3. Give your passport at the desk, you will be asked why you want the check (as they can granted for jobs and all manner of requests) you should say "Ikamet" (residence permit)
4. Take your printed piece of paper from the clerk and sidestep to the desk that says IMZA (signature), present the paper for a no doubt higher paid clerk to sign it and stamp it. The check is free for residence permit purposes.
Oh and maybe check it to make sure you record is clean too before putting it in your application ;)