Is taking profits from an on-demand investment account at Bank Misr's Islamic Transactions Branch permissible (halal) or forbidden (haram), keeping in mind that the parent bank is interest-based (ribawi) and the branch claims to operate according to Islamic Sharia, but without clarity regarding the investment method or the presence of Sharia supervision, and given that this branch is the only one available with an Islamic system in the governorate?

It is permissible to deal with a bank branch if it adheres to the rulings of Sharia in its transactions, and its investment channels are separate from the usurious bank, and it does not use this as a cover to attract funds and exploit people's emotions and their aversion to forbidden usury. Otherwise, it is not permissible. To ascertain the extent of the branch's compliance, you should ask reliable scholars in your country. If you do not find anyone who can remove your doubt, then piety dictates avoiding dealing with them, based on the hadith: "Leave that which makes you doubt for that which does not make you doubt." Money can be deposited in trustworthy Islamic banks or invested through Mudarabah and similar permissible forms of investment.