You can pay your MCC counselling fees via any digital recognised mode like credit card debit card or net banking. So,if you have your Andhra Bank account's debit card or it is registered on net banking then you can easily use it for fee payment so it does not matter whether it is Andhra Bank ,SBI or any other government recognized Bank .You just need to pay through your Credit Debit card or net banking.
List of colleges you can get after MCC counseling on the basis of your Neet rank use Neet college predictor tool:

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer