What is the duty of a mature son if his father's money is mixed with suspicion of haram (such as bribery and reducing specifications in work), and is it permissible for him to use this money for his studies and his lawful trade?

Scholars have differed regarding eating from lawful wealth that has become mixed with unlawful wealth. The preponderant opinion is that it is permissible to eat from it if the lawful portion is dominant, and disliked if the unlawful portion is dominant. One should intend, when eating, to be eating from the lawful portion. As for wealth that is entirely unlawful, it is not permissible to eat from it or benefit from it at all. Therefore, it is permissible for you to benefit from a portion of your father's wealth with the intention of it being from the lawful part.