My question is that my father is able to fast but they don't fast. Is it necessary to do kaffara on behalf of him is wajib on me?

You cannot do so long as he is life. Encourage him to fast. Otherwise, you will pay on his behalf once he departs from this world. Note: if your father ignores his salat intentionally and without any valid reason, you will not be obliged to pay back. However, it will be good to pay back since he is your father.
It becomes wajib if it’s not out of negligence