Hello Aspirant

You may have read the notice wrong because in the NEP 2020, it is nowhere mentioned that private candidates cannot appear for NEET.

The eligibility criteria for NEET is that the candidate must have passed Class 10 or equivalent with at least 60% aggregate marks and be appearing for Class 12 or have passed Class 12 with Physics, Chemistry, and Biology as compulsory subjects. That's it. Nothing has been mentioned about the Board of Examination. You can appear for NEET despite being a private candidate.

Hope this helps