What is the appropriate action to take towards an unjust father who favored one of his sons (who does not pray and is a drug addict) in the inheritance over his other children, even though the favored son is wealthy and some of those deprived are poor?

It is your duty to honor your father and treat him well, for his right is great and is not nullified by his wrongdoing or mistreatment. Allah has commanded us to accompany even polytheist parents with kindness. Honoring him includes advising him, deterring him from injustice, clarifying that a will in favor of an heir is impermissible, and enjoining him to be fair among his children, all with gentleness and respect, without harshness, for the matter of parents is not like that of others.