What is the ruling on swearing falsely upon the Qur’an knowingly, and what is its expiation? Does it differ from swearing by Allah? Is it obligatory to avoid it even after expiation?

Whoever swears by the Qur'an or places their hand on it and swears by Allah falsely has committed a "ghamoos oath" which immerses them in Hellfire. Their action increases in sin, and they must repent and seek forgiveness. According to some scholars, an expiation for the oath is obligatory: it is either the freeing of a slave, or feeding ten needy persons, or clothing them. If one is unable, then fasting for three days.