Is it obligatory for a son to continue praying Fajr in congregation despite his parents forbidding him, knowing that his parents strictly prevent him, and would his mother's supplication against him be answered in this case?

Congregational prayer is obligatory, and it is not permissible to miss it except for an excuse. If your parents' fear for you from harm is merely an illusion, then you are not obliged to obey them in abandoning the congregation, because there is no obedience to a creature in disobedience to the Creator. However, if it is highly probable that harm will occur, and they forbade you out of compassion, then you must obey them, and you can pray in congregation at home. Be keen to earn your parents' satisfaction, for in it is the satisfaction of Allah.