I work a part time job putting in 10 hours a week, when I started this job I filled out a W4 form letting my employer know that I am claiming zero and wanted the maximum amount taken out.
I just got my W2 from this employer and the only taxes taken out were for social security and medicare. They were telling me that because I was part time that they are not required to take out federal and MN withholding?
I am pretty sure this is not true and can you help me on this question Thank you

Your employer is right.

The amount taken out is based on your income, which, being part-time, would not be much.

So it is likely the employer is correct.