According, to officials in order to apply for JEE Main application form you should submit a correction request at Aadhaar centre and apply for JEE (Main) by entering 14 digits Aadhaar Enrolment ID/UR No. (Including slash) printed on the slip issued by aadhaar centre after submitting updation request. Or Such candidates should fill the form of JEE (Main) with old details in Aadhaar card and thereafter submit a correction request at Aadhaar centre. The updated details in Aadhaar may be corrected in JEE (Main) at later stage by the process which will be notified in due course of time.

Good Luck!!