Is it correct to give a quarter of a tithe from cash in the bank as zakat?

If you have given 2.5% of your money in the bank as zakat (definition), then your action is correct; because the obligatory amount for cash that has reached the nisab (definition) and for which a full year has passed is a quarter of a tenth. Zakat must be distributed to the eight categories mentioned in the verse from Surat At-Tawbah (definition): "Indeed, zakat expenditures are only for the poor and for the needy and for those employed to collect [zakat] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler - an obligation [imposed] by Allah. And Allah is Knowing and Wise."