If you are a UT resident and have income, you have to file a UT Resident Tax Return and report all of your "world-wide" income.

If you NEVER go to NY but are paid by a NY company, you have no NY source income.  You therefore have no requirement to file a NY Non-resident tax return.

If you are somewhere in between you should develop some sort of defensible method to allocate your income between UT and NY.

On your NY Non-resident Tax Return you report only the income from when you were actually in NY. The taxes you pay to NY are then credited to your UT tax return as taxes paid to another state so you are not taxed twice on the same income.

If your NY W-2s have NY withholding you will need to file a NY Non-resident Tax Return in order to get that withholding refunded to you.