Hello aspirant!
Hope you are doing well!

Yes you can apply for the state quota counselling but you have to fill and register in the respective state counselling form available in the official website,
For more information refer to the article
NEET 2020 Counselling FAQs - All India Quota, State Quota & Others
https://medicine.careers360.com/articles/neet-counselling-faqs

Hello aspirant

Hope you are doing well

Yes, you can apply for both AIQ counselling and State counselling..

First, you have to register for All India Counselling which is done by Medical Counselling Committee(MCC)  And After the  first Round of AIQ Counselling, the Round first for State Quota Counselling has been  started ..

After the completion of this, the 2nd Round for AIQ has been started ,and if you are not getting seat in AIQ than you can apply for 2 round state counselling  StateCounselling..

Because, the state counselling process has been stared only after the completion of AIQ counselling..

Hope you find this information useful and will help you to solve your query

For more information about counseling you can check this link

https://medicine.careers360.com/articles/neet-counselling/amp