What is the ruling on interest and profits added to money inherited by a minor and placed under the supervision of the state in an Islamic bank, after the minor reaches the age of majority?

If the money is deposited in an Islamic bank, there is no harm in benefiting from its profits. Zakat is obligatory on the money that reaches the nisab (minimum threshold) if its zakat for past years has not been paid immediately, because it is a debt that does not lapse with time. Whoever delays paying zakat without a legitimate Sharia excuse has sinned, and must pay it for all the overdue years. If in doubt, one should act based on their best judgment in estimating the amount of money and the number of years.