What is the expiation for someone who deliberately swore falsely by Allah during the daytime in Ramadan while fasting, and what is the ruling on their fast?

You intentionally took a false oath (Yamin Ghamus) during the daytime in Ramadan, which is a lie that does not invalidate the fast according to the majority of scholars. However, sincere repentance (Tawbah Nasuh) is obligatory. If this act resulted in taking a Muslim's right, it must be returned. It is more prudent to perform the expiation for an oath (kaffarat al-yamin).