There is Bank X belonging to the government that operates conventional and Shariah (Islamic law) separately but the owner of the bank is same (government). The question is it Halal to work and to deposit in that bank that operate Shariah?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If you are certain that the Islamic section branch of the bank is abiding by the Shariah rulings and that all its investments are separate from the interest and usury branch of the bank, that the latter does not use the Islamic branch to attract people's money and exploit their feelings, that it really rejects interest and usury that Allah forbade in His Book and that the Prophet (Sallallahu Alaihi wa Sallam) forbade in the Sunnah, if the matter is as such , then there is no harm in dealing with this branch by saving money or other transactions.

The Prophet (Sallallahu Alaihi wa Sallam) and his companions used to deal with the Jews (in buying and selling) and in other permissible transactions, and it is known that the Jews deal with usury and interest.

Allah knows best.