If you are a J-1 student you must provide a letter from your sponsor and should be on the letterhead of the sponsor with original signature that authorize employment.
What documents do I need to show child's U.S. immigration status?
You must provide your child's current U.S. immigration document such as I-551 Lawful Permanent Resident Card, Machine Readable Immigrant Visa or I-766 Employment Authorization Document, work permit.