Hi I am a non-resident of NYC, I am an NH resident, why am I not getting my City tax back? it is saying something about a school district.

Do you mean that NYC tax was withheld from your pay? Are you saying that on your W-2 you have local income tax in box 19 and NYC in box 20?

If you live in New Hampshire, why was any NYC tax withheld? If you were not a NYC resident at any time during the year, and your employer knew that, then withholding NYC tax is the employer's error, and the employer should correct it. Were you previously a NYC resident and did not notify your employer that you moved? Or did you give the employer a NYC address even though you don't live there?

It seems unlikely that you are commuting from New Hampshire to New York City. Did you work remotely, and New York State treats you as working in New York? Even if you physically worked in New York City, nonresidents do not pay NYC tax.

"it is saying something about a school district."

What is "it" that says something about a school district? Are you working on a New York nonresident tax return? What is the complete exact message about the school district, word for word? A full-year nonresident does not enter a school district. Were you a part-year resident of New York State?