If you have one back paper in 12th, your eligibility to participate in NEET counseling rounds (including mop-up rounds) depends on the rules of the specific state or counseling authority.

Generally:

You must have cleared all 12th subjects (no backlogs) to participate in the main NEET counseling.

If you still have a back in one subject and haven’t cleared it yet, you are usually not eligible for counseling.

In some states, you can participate in the mop-up round only if you have cleared your back and have a passing result before the counseling starts.

So, you can take part in all NEET counseling rounds only after your back paper is cleared and you have passed 12th.

I can also check the specific rules for your state if you want!