What should one do if their father accused them of being an "illegitimate child" and wished cancer upon them, even though they are dutiful towards him?

A father should treat all his children equally in everything, including emotional matters and gifts. If he favors some over others without a legitimate Shar'i reason, he is sinful or blameworthy. The son, on the other hand, must honor and treat his father well and not be disobedient to him, even if the father falls short in his duty towards him. Your insolence towards your father and raising your voice at him is an act of disobedience that requires repentance and an apology to your father.