What is the expiation for an al-yamin al-ghamūs (a false oath sworn deliberately to usurp another's right) after swearing falsely about an act that has already been committed, and is seeking forgiveness (istighfar) sufficient?

If a mother forbids her daughter from doing something in the future, and then the daughter swears not to do it, if her oath was a slip of the tongue without intention, it is considered a laghw al-yamin (a thoughtless or unintentional oath) for which there is no expiation. However, if she intended the oath and committed to it in her heart, then expiation is required.

As for the daughter swearing that she did not do something in the past when she actually did it, this is a yamin ghamoos (a perjurious oath), which is a lie for which there is no expiation. Repentance for it is only required, according to the majority of scholars.