Can I fast three days as an expiation for an oath on behalf of my father, who swore an oath and then broke it, given that he is unable to fast due to the hot weather and diabetes, even though he fasted the entire month of Ramadan?

The expiation for an oath is: freeing a slave, or feeding ten needy persons, or clothing them. And for whoever cannot find [any of these], then fasting for three days. Fasting is only valid for those who cannot find the other options. Your fasting on behalf of your father is not valid. If your father was unable to feed, clothe, or free a slave, but was able to fast, then fasting becomes obligatory for him. If he was unable to fast, then the expiation is waived for him.