The year is nearly over so at this point it will not make a difference for 2019--but you can ask your employer to let you correct your W-4 so that you are not claiming exempt any more. Use "0" or "1" for the number of allowances you claim on your W-4. If you are a teenager with a part-time job, that you just started, you are highly unlikely to have a tax liability for this year, so no harm done.
If no tax is withheld -- which is what happens when you claim to be exempt -- then you will not receive a tax refund. You never get a refund for the Social Security or Medicare withheld, but if you have some federal and state tax withheld, you can get a refund at tax time.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
