Is expiation obligatory for one who swore by his mother's mercy while angry, and what is the expiation for this oath if he intends to retract it?

Swearing by other than Allah is forbidden and does not necessitate an expiation. Rather, you must seek forgiveness and repent. Ibn Qudamah said: "Swearing by other than Allah is a sin, and a good deed erases a sin, as the Prophet (peace and blessings of Allah be upon him) said: 'Whoever swears by Al-Lat and Al-Uzza, let him say: "There is no god but Allah."'" Furthermore, harming others through beating or otherwise is forbidden, and you must retract this intention, and no expiation is required of you.