CT applies the "convenience of the employer" rule only to non-residents who reside in states that themselves have that rule.
Since NJ does not have the "convenience" rule, income you earn by working remotely from an NJ location is not subject to CT income tax. (But if you were to perform any work from a location inside CT, the income from that work would be taxable by CT.)
If you as a non-resident of NY work for a CT employer, and never physically work from a location inside NY for the entire tax year, then your work income is not taxable by NY.
ALL your income is of course taxable by your home state of NJ, regardless of where earned.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
