New York City income tax only applies to NYC residents. She would not be a NYC resident if she was in NYC to attend school.
Attending school is considered a temporary absence so your daughter remains a California resident unless she moved permanently to NY in September.
California residents pay taxes on income earned anywhere during their period of residency.
File a full year California resident return and a full year nonresident New York return. Report all income on the CA return and only NY income on the NY nonresident return.
You can claim a credit for tax paid to NY on the CA return.
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