No. NJ as your resident state taxes all income from all sources. You will however be able to claim a credit for taxes paid to NY on the 20% of income.
First complete the NY interview and take note of the income taxed and what the taxes paid to NY were. You will use that to complete the NJ interview section for the "Credit for taxes paid to another state".
Be aware of NY's rule regarding non-residents who normally work in NY, but who are now telecommuting due to Covid:
If you are a nonresident whose primary office is in New York State, your days telecommuting during the pandemic are considered days worked in the state unless your employer has established a bona fide employer office at your telecommuting location.
https://www.tax.ny.gov/pit/file/nonresident-faqs.htm#telecommuting
This means that 100% of your income may still be taxable by NY.
Take a look at your W-2, were state taxes withheld for NY or NJ? If NY, all your income is considered NY-source income and you pay income tax to NYS. But you will receive a credit for taxes paid to NY on your NJ state return. At the end, if you have no NJ income, the taxes paid to NY give you enough credit to reduce your NJ taxes to minimal.
Always prepare the NYS return first, taxes paid to NY will carry over to NJ properly.
@FangxiaL My state tax withholding was NY, then once my working location was changed to NJ the withholding changed to NJ as well.
If your office location changed to New Jersey, then the income is no longer New York sourced. Allocating 20% of your income to New York would be accurate. As stated above, New Jersey will tax all of your income as a resident. However, your resident state will give you a credit of taxes paid to New York for your double-taxed income. The double-taxed income in your situation is the 20% earned in New York.
@Anonymous