Hello @ittigorn

Before a transaction settles, your only option is to Void the entire transaction.  After a transaction has settled, you can refund (credit) using the previous transaction ID.  

These are the relevent API Methods:

http://developer.authorize.net/api/reference/index.html#payment-transactions-charge-a-credit-card

http://developer.authorize.net/api/reference/index.html#payment-transactions-void-a-transaction

http://developer.authorize.net/api/reference/index.html#payment-transactions-refund-a-transaction

Richard