As-salāmu ʿalaykum. Ahsana Allahu ilaikum. My father (may Allah bless him) has aggressive manners. Alhamdullilah, my family are patient. He acts this way to my fiancé and if I am present I put my head down out of embarrassment. I fear it may affect my engagement. Please advise me.

There is no such thing as a "fiancée" in Islam in the Western sense, where you sit with her multiple times. But if you mean that you went once or twice to sit with her before both of you accepted the marriage, sitting with her in order to do (the Islamic look), to talk to her, and so on, and both of you have accepted but the marriage is yet to happen, then that is enough. Therefore, she wouldn't need to see how aggressive your father is at this stage. After you marry her, inshallah, separate her from your father and his aggressiveness, and minimize their meetings as much as you can to avoid problems.