Permanent TSB holds £20.2m worth of deposits in an Isle of Man subsidiary, according to the bank.
The figures are contained in a Department of Finance response to a parliamentary question by Fianna Fáil's finance spokesperson Michael McGrath, who asked a series of questions in relation to the offshore operations of the country's bailed out banks.
In its response PTSB said it had had two operations in the Isle of Man - Irish Permanent (IOM) Ltd, which ceased operations in 2010 and Permanent Bank International Ltd, which is in the process of being wound down.
The latter is set to surrender its banking licence at the end of this year however 223 of its accounts, with a total balance of £20.2m, have yet to be closed.
AIB said its two businesses based in Isle of Man and Jersey - AIB ISL and AIB CI - ceased operations at the end of 2013.
The bank then established separate accounts to handle any unclaimed balances, with remaining depositors becoming creditors in the new entities.
Those accounts are administered by Estera Trust and as of last year had a combined 420 customers with a total value of £13.6m.
In response to Mr McGrath's questions the Minister for Finance Paschal Donohoe said Revenue was aware of the details of the 'Paradise Papers' and would examine any issues relating to Irish individuals or entities.
Mr Donohoe also defended Ireland's tax system and said that it was "damaging and inaccurate" to suggest that the country was responsible for the international tax arrangements of multinational corporations.
He said Ireland had taken "a number of steps towards implementing the BEPS Actions", would also implement the European Union's Anti-Tax Avoidance Directives and had maintained a high level of tax transparency.