I live in New jersey and work for 2 different employers (i.e have 2 different jobs). My full time employer is based in my state of New Jersey (has no connections with New York state) while my part time employer is based in New York.
I intend to file a resident income tax for New Jersey and a non resident tax for New York state. However, I was wondering if New York would tax based on my total income (ie. NJ income +NY income) or just for the income from the State of New york (since the my New Jersey employer has no relationship with New York state)

New York will tax you only on your NY-based income.

For NY to tax you (a NJ resident) on your NJ income is against the law.