If your state of residence is NJ, all your income is taxable by NJ.
Money you earn by physically working in NY, or that you earn by working remotely for an NY-based employer for your own convenience (as opposed to the convenience of your employer) , is also taxable by NY. Your obligation to file a NY tax return is determined by the amount of your NY-source income, not by the number of days you spend working in NY.
You'll be able to take a credit on your NJ return for taxes paid to NY, so you won't be double-taxed.
Note: A bill has been introduced in the New York Senate (Bill S-8386) which would designate remote work done outside the state due to COVID-19 as being for the convenience of the employer, and thus not taxable by NY - but the bill has not yet passed as of today (August 8).
Thank you @TomD8. Do you know what the NY-income source threshold is and how it’s determined? My company is reducing NY office space thus my job is officially becoming mostly remote where I would only come in 4-5 times/month for big meetings.
The web link in my previous answer will take you to the NY website where you can find the detailed info on both your questions.
Basically your NY-source income consists of:
1. the income you earn on the days you physically work in NY, plus
2. the income you earn when you work remotely from NJ by your own choice.
Income you earn when you work remotely from NJ because your employer requires you to do so is not NY-source income.