Prabhu, even Private Candidates are eligible for NEET. Now there is no upper age limit for NEET. NEET 2020 will be held in the month of May and the counselling and admission process will begin tentatively from the month of August. You should be able to complete your 12th and pass in all subjects by then. And based on your Category, you should score a minimum aggregate of 50% in Physics, Chemistry and Biology. It is 50% for General Category, 45% for PWD and 40% for OBC,SC,ST. Now there is no age bar for NEET. So if you can manage to clear the backlog by the month of July atleast you can join Medical College based on your NEET score. Until then you can appear NEET 2020 as well. In other words, even if you have a backlog and you will appear for the exam in March 2020, you are eligible for NEET 2020.

Hello student don't get frustrated calm down yes you're eligible even when you're appearing in class 12 cbse exam as a private candidate you can apply for neet 2020 as eligibility criteria says that - Candidates must have passed 10+2 or equivalent with Physics, Chemistry, Biology/Biotechnology and English as core subjects from a recognized board. Candidates who are appearing for the class 12 or equivalent exam are also eligible to apply for NEET 2020.

Just be calm and start preparing for both of your exams as they're knocking at the door.

Feel free to comment if you have any doubt
Good luck