Hii aspirant,

If your name in caste certificate is wrong there is a temporary solution to it, you can fill the student undertaking form at the time of registration which states that you are eligible for the benefits of reserved categories and would produce the certificate by the time. Later on you can apply for a new caste certificate after 1 April that would be considered valid for JEE advanced examination. In case you are only considering  JEE main you would need to upload the certificate at the time of counselling to avail its benefits.

Hope it helps!