Is the father required to do anything because he uttered an offensive word against Allah during a quarrel in Ramadan three years ago, knowing that he has forgotten the incident but the son remembers it now?

If the word was uttered by the father while he was in a state of absentmindedness, then there is no sin upon him. However, if it was uttered consciously and knowingly, and it constituted a curse against Allah, then it is apostasy. If he pronounces the two testimonies of faith or prays thereafter, he returns to Islam, and he must make up the day on which he apostatized, because apostasy invalidates the fast. He should be reminded of the ruling of the Sharia in this matter with gentleness and kindness.