Hello. I live in NJ and work for a NJ Employer. My current assignment is working as a consultant for a NY based company thru my NJ employer.
Situation 1: Due to Covid, I have not travelled to NY client location to work at all.
a. Do I need to file NY State Tax Return and pay NY Income Tax in this situation?
Situation 2: If I do need to commute to NY under same circumstances later in the year:
b. Will I then be required to file NY Tax Return and pay NY Income Tax?
No, given that your employer is a NJ Company and you are a NJ resident, you are not required to file in NY as this is just the location of your employers' client and not your "place of work", so to speak.
Example: I am a RI resident and I previously worked for a NH Consulting Firm for 4 years. During that time, I worked for multiple different clients of this consulting firm in many different States - including some out of the US. Now, if NH were not a "no state income tax" state, then I would have had to file my RI Resident ITR and a NH Non-Resident ITR. In your case, you live and work (by definition) in the same state (because your employer is a NJ employer), so you would have NJ withholding and NJ is also your state of residence, therefore you are only required to file in NJ for your State Income Taxes.