What is the ruling on the fatwa that permitted a guardian to fast instead of feeding the poor as expiation for an oath, given that it includes the meaning of deterrence which is not achieved by feeding?

We have not come across this specific issue. However, the expiation for an oath allows for a choice between feeding ten poor people, or clothing them, or freeing a slave. If one is unable to do any of these three, then they must fast for three days. This is what the scholars have agreed upon. In a similar incident, Yahya ibn Yahya al-Laythi issued a fatwa to the Amir of Andalusia to fast as expiation for intercourse during Ramadan, in order to deter him from repeating the act, even though the Maliki school offers a choice between freeing a slave, fasting, and feeding. Nevertheless, the majority view is that the expiation here is also in sequential order.