I am a Massachusetts resident and did my internship in New Jersey. I got a w2 from my internship employer which was information on front and back page. Front oage has all boxes related to federal wage

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If Massachusetts is your domicile and you are filing state income taxes as a Massachusetts resident, all of your income, wherever earned will be taxed.

The State of New Jersey will expect you to file as a non-resident and pay taxes on the internship income that you earned there.

Massachusetts will allow you a credit for the taxes paid to New Jersey.