Praise be to Allah.
Your working in this bank is haraam, even if you are in a department which does not deal with riba-based transactions. It is sufficient to note that the “central bank” is the head bank and working in the other departments complements the work of the sections that do deal with riba; the bank is formed from all the departments and all the institutions connected to it are engaged in riba.
The scholars have stated that it is not permissible to work even as a guard or driver for such institutions, so how about working as a teller or clerk?
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: It is not permissible to work in a riba-based institution even if a person is working as a driver or guard, because that means that he is working for the riba-based institution, which implies that he approves of it. For whoever disapproves of a thing would not work to support it, so if he is working for it that implies that he approves of it, and the one who approves of something that is haraam is also guilty of sin.
But if he is directly involved in recording transactions, writing, sending and depositing etc, then he is undoubtedly dealing directly with something haraam. It was proven in the hadeeth of Jaabir (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) cursed the one who consumes riba, the one who pays it, the two who witness it and the one who writes it down. He said: “They are all the same.”(Fatawa Islamiyyah. 2/401 )
The Standing Committee was asked about a man who worked as a night guard for one of the banks, and he had nothing to do with the bank’s transactions – should he continue with this job or leave?
It is not permissible for a Muslim to work as a guard for banks that deal with riba, because this is a kind of cooperating in sin and transgression, and Allah has forbidden that as He says (interpretation of the meaning):
“but do not help one another in sin and transgression” [al-Maa'idah 5:2]
Most of the banks deal with riba, so you have to look for a halal means of earning a living, not this way.
And Allah is the Source of strength. May Allah bless our Prophet Muhammad and his family and companions.
Fatawa Islamiyyah, 2/401, 402
And Allah knows best.