Does expiation become obligatory for one who swore an oath not to hit his son, while intending to hit him, and then hit him?

It appears that you swore a false oath by Allah, and this is a "yamin ghamus" (a deliberately false oath sworn by Allah). Repentance is required for it, and according to the majority of scholars, no expiation is due. However, if you wish to be cautious, you may offer the expiation for an oath. Hasten to repent to Allah Almighty, and do not return to such false oaths.