Allied Irish Bank has confirmed to RTÉ News that it is to make refunds to 34,000 of its third level and graduate customers.
The bank says the total amount of money to be refunded before interest compensation is in the order of €1.4m.
The money is being refunded because certain advertised discounts to students were not applied in all cases.
Fine Gael described the revelation as a scandal and accused the bank of being evasive in its approach to informing the public.
The party's Enterprise, Trade and Employment spokesman, Phil Hogan, said the sequence of scandals emerging from AIB was jeopardising the credibility of the Irish financial sector.
Labour's finance spokeswoman Joan Burton said the Irish banking sector was rapidly losing the confidence of the Irish public.
She said some in the financial sector had refused to learn their lesson and were still prepared to squeeze every possible cent out of their customers by fair means or foul.
The Irish Bank Officials Association said AIB staff would be saddened and disappointed by the latest disclosures.
It called on the Irish Financial Services Regulatory Authority to complete its investigation into overcharging of AIB customers as speedily as possible.
The President of the Union of Students in Ireland, Ben Archibald, said the news was worrying but said students would be pleased the bank was attempting to make reparation.
