If someone has missed some fasts and should perform some fasts of his father, it is up to him to perform either at first.

To Make Nadhr to Fast While Having Some Missed Ones
A person, who has missed some fasts during Ramadan month, may make nadhr to fast provided that he intends to perform it after performing his missed fasts.

To Delay Qaḍā’ Fast of Ramadan
If someone does not make up for missed fast until next Ramadan due to illness, making up for them ceases to be obligatory but they should pay fidyah. In case it is delayed due to an excuse other than illness, which prevents them from fasting, it suffices to make up for missed fasts; yet it is a caution to make them up and pay fidyah (one mudd, i.e. 750 grams, of food) as well.