Is it permissible to feed ten orphaned infants milk as an expiation for an oath, knowing that they consume nothing but milk? And is an father obligated to offer expiation for an oath made by his adult daughter who is under his guardianship?

A father is not obligated to pay the expiation for an oath (kaffarat al-yamin) on behalf of his adult daughter, even if she is under his financial care. If the daughter does not possess money for the expiation, she must fast for three days, as Allah Almighty says: "But whoever finds none, then a fast of three days" (Quran 5:89). She is not obligated to ask her father for money. The expiation is not considered part of financial support. However, if the father voluntarily pays it, that is good. As for paying the expiation to an infant in the form of milk, it is not sufficient. Scholars have differed regarding the sufficiency of paying it to a child who does not eat solid food. Some have prohibited it because the child does not eat, while others have permitted it, stipulating that it be spent on the child's welfare. This is the madhhab of Imam Shafi'i and most jurists.