What is the ruling on inherited wealth that includes usurious gains, and how can this wealth be purified, knowing that a portion of it has already been disposed of?

Bank profits (interest) are Haram (definition) by consensus because they are a loan that brings benefit. Whoever has engaged in them must repent and spend these profits on charitable causes. If the father dies before disposing of them, the heirs must dispose of them, and it is not permissible for them to inherit them. As for the mother, you are not required to give anything from her money if she does not take interest, but it is recommended to check her account statements. Zakat (definition) is not obligatory on these profits because they are not owned. Whatever was consumed from them before knowing their unlawfulness does not need to be given out, based on the Almighty's saying: "So whoever receives an admonition from his Lord and desists, he may have what has already passed, and his affair is with Allah." You are not required to pay Zakat from your father's wealth if he was diligent in paying it, unless you know that he did not pay it after it became due.