Hey,

No, registration with State counselling will not affect your All India Counselling results.

Suppose you get a seat in the first round of All India Counselling and you join it, you can also exit the seat if you get a seat in a better college through state counselling.

But, if you join a seat allotted in the second round of All India Counselling then you cannot leave the seat.

To get a list of colleges in which you can get a MBBS/BDS seat, you can use NEET College Predictor https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer