I filled jee main exam form, unfortunatly i did mistake in my parent;s name.and now correction also closed. what i can i do?

Since nothing can be done now, it is better to go ahead with the exam. But get an Affidavit from the court and file it officially with the board alongwith an application stating the truth so that it may be handly to you at the right time and correction be made later. The method might not work to sat