Does Allah take revenge on children for their father's unrighteousness by closing doors of provision to them and afflicting them with illnesses?

A person is held accountable for their own deeds, not for the deeds of others, even if that other is their father or a relative. The proof for this is that Abraham's father, Noah's son and wife, and Lot's wife were disbelievers, yet the prophets were not held accountable for the sins of their relatives. The fundamental principle is that punishment or reward is for the one who performs the action or commits the forbidden act, and this is the justice upon which the heavens and earth are established, and which is affirmed by the laws of all prophets. Allah Almighty says: "That no bearer of burdens will bear the burden of another, and that there is not for man except that for which he strives, and that his striving is going to be seen - then he will be recompensed for it with the fullest recompense" (An-Najm: 38-41). And Allah Almighty says: "And no bearer of burdens will bear the burden of another" (Al-An'am: 164). That is, no soul will be held accountable for the transgression of another, as Allah Almighty says: "For it is what it has earned, and against it is what it has incurred" (Al-Baqarah: 286), and "Every soul, for what it has earned, will be detained" (Al-Muddaththir: 38).