Heyy
To get admission in private medical college in UP you should be a domicile of UP first. Private colleges fill seats on the basis of state quota only and not through all india quota. Then you have to go for 1st round with your preferances and choices. If you cannot get college in 1st round then only you will be eligible for 2nd round. If you belong to reserved category like OBC/SC/ST then you might get private medical college in the first round only. If you belong to general category then you might get college in 2nd round or so.
Goodluck

Dear student, you have secured enough marks in NEET UG 2019 to secure a seat in some of the good private medical colleges in Uttar Pradesh. With 423 marks, you must participate from the round 1 of counselling process. You are fair chances to secure a seat in Muzaffarnagar Institute of Medical Sciences in the first round itself.