If opening the account in this bank was done out of necessity for the transfer of wages and the like, that is permissible because of necessity and there is nothing wrong with you paying fees to the bank in return for that, because it is only paying fees for the transfer.
The scholars of the Standing Committee said:
Depositing money in riba-based banks is not permissible. With regard to transferring money through the bank, if the request comes from the company and there is no other bank apart from the bank that is riba-based, then it is permissible to make the transfer through the bank because of necessity. End quote.
Fataawa al-Lajnah al-Daa’imah, 13/372; see also: Fataawa al-Lajnah al-Daa’imah, 13/370.
Shaykh Ibn Baaz (may Allah have mercy on him) said:
If it is necessary to transfer money via the riba-based bank, there is nothing wrong with that in sha Allah, because Allah says (interpretation of the meaning):
“He has explained to you in detail what is forbidden to you, except under compulsion of necessity”
Undoubtedly transferring money through the bank is a very common necessity nowadays.
If it is possible to make the transfer through an Islamic bank or through permissible means, then it is not permissible to do the transfer through the riba-based bank. The same applies to making deposits; if it is possible to deposit money into Islamic banks or Islamic businesses, then it is not permissible to deposit it in riba-based banks, because it is no longer a matter of necessity. End quote.
Fataawa Islamiyyah, 2/879
It is not permissible to open an interest-bearing account in the bank with the aim of paying off the fees charged by the bank for its work, because the prohibition on riba is not for the sake of the bank, so that we can take from it and give to it; rather the prohibition has to do with the rights of Allah, whether we are going to pay it or not, and whether the original transaction is permissible or forbidden. None of that makes it permissible for us to engage in a haraam transaction in order to pay the fees for the original transaction.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked:
Is it permissible for me to make a deposit in the bank in return for interest in order to pay taxes that I have to pay as a result of this interest?
He replied: That transaction is not permissible, because it is a riba-based transaction that it is not permissible to do, because Allah says (interpretation of the meaning): “Allaah has permitted trading and forbidden Riba” [al-Baqarah 2:275]. End quote.
Majmoo‘ Fataawa Ibn Baaz, 19/211
And Allah knows best.