I wrote my caste wrong in jee application.error correction date was completed.my principal said that take caste certificate to exam hall .

You needn't validate your Category during the written exam. You needn't show any proof of your category to the invigilator. You will need your admit card and an id proof. Now the problem arises only during your counseling. Say if you get a bigger rank but because of the category you chose, you get merit and move to a smaller rank and get a seat in a good college, you will have to prove your category through which you benefitted. For example if you belong to OC but chose SC by mistake and fidndi correct it, the application form will show that you belong to SC category. Your invigilator in the exam hall wouldn't even bother your category. He/she is more concerned whether you brought your admit card and I'd proof. That's it. Now say you got some 12000 rank but because you chose SC, you get a merit and are considered for 600 rank, you will get admission into a very good college. But now at the time of counseling, you need to show them the proof of your category that you truly belong to SC. At that point, you cannot tell them that you chose the category by mistake and correction window was over. Though you didn't do it on purpose, your admission will stand cancelled and you might be booked on malpractice. You will not be considered even on OC category. You will lose a year. Not to scare you, but it is too late for correction and too late for re registration.