Dear Hima, AP NEET Counselling has 2 rounds of Counselling for Convenor Quota seats and 1 round for Management Quota seats. There is no 3rd round for Convenor Quota seats. There ia a mop up round for unfilled, vacant seats left over after Round 2 of All India Counselling and remaining seats after State NEET Counseling. This will start tentatively in the month of August after the seats are transferred from Central Pool. With 409, you might have a chance in any Private Medical College depending on the area you are a local to. It might be difficult if you belong to AU area but you have a chance if you belong to SVU area.