What should I do with the inheritance I received from my father, knowing that the source of this money is mixed between his salary, his stock market speculations, and usurious interest from investment certificates, and its value increased after selling the house? My father bought me an apartment with half of my share of this inheritance, and the other half remained in a deposit?

The apartment your father bought for you is a gift, not an inheritance, and it is permissible to accept it even if your father's money is mixed (with unlawful earnings). As for inheritance, money acquired through unlawful means must be separated from it before division. If it is impossible to identify it, half of the money should be removed. If the house your father sold had unlawful money involved in its construction, then only the unlawful portion should be removed, while the increase in price belongs to him. There is also an opinion that money that is inherently unlawful is only forbidden for the one who acquired it, and not for someone who acquired it from them through permissible means. According to this view, the heirs are not required to remove usurious gains from the estate.