Federal taxes are not being taken out of my check I work for a public school as a food service worker. I claim 3 and make about 12,000 yearly

Medicaid, or do you mean Medicare?

Medicaid ok so my income is to low that is why. what does the yearly income have to be where they salary start taking income tax out. thank you for answering

See tables at the end of this publication:
<a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p15.pdf">https://www.irs.gov/pub/irs-pdf/p15.pdf</a>

Your income is too low for Federal taxes to be withheld.

If $12k is your total income for the year, you will owe no taxes.

thank you for your answer what would be the minimum income in which they would start taking taxes out?

Look at the table in the link I gave in the comments.

Some local public employees are exempt, by law,  from social security tax (box 4 on your W-2).  School employees are a common example.
The rationale is that your contributions to teacher (public employee) retirement are a substitute for social security.