What should I do regarding a person whose car I accidentally scratched, and my father denied knowing about the incident when the car owner asked him, to which the owner said, "I will take it from you on the Day of Judgment," and I do not know this person to compensate him?

If you are the one who scratched the person's car and did not inform your father, then you are responsible for compensating him, not your father, and he has no obligation towards him. If the scratch is of real value and the owner of the car cannot be identified, then give the money in charity on his behalf.