Hello,
Date of Birth certificate is a compulsory document required for state quota seats. As it mentions the date and place of your birth and hence confirms your belonging to that state.
Without it you will not be eligible for state quota seats.
It can be issued within a week. Contact your regional UIT Office/paarshad/regional authority for the same.

For more documents related query follow this link:
https://www.google.com/amp/s/medicine.careers360.com/articles/neet-counselling/amp

Good Luck!

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