My father can neither fast nor give food to a needy person because he is old and sick. We cannot afford to give food to the needy in expiation. Is it permissible for me to fast on behalf of my father?

All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

We implore Allaah The Almighty to cure your father from all diseases. It should be noted that if your father is permanently unable to fast, it is obligatory on him to feed one needy person for every day of Ramadan on which he does/did not fast.  Allaah The Almighty Says (what means): {And upon those who are able [to fast, but with hardship] - a ransom [as substitute] of feeding a poor person [each day].} [Quran 2:184] If he is unable to give food to the needy as expiation, he is not required to do anything else in this regard. In Al-Mughni, Ibn Qudaamah, said, "If a man is unable to give food, nothing will be obligatory on him in this regard, and Allaah The Almighty does not burden a soul beyond its capacity."

If your father could afford it at a later time, expiation will be obligatory on him then. It is not permissible for you to observe fasting on behalf of your father because every soul will only be accounted for what it did. Sharee‘ah evidences support fasting on behalf of the dead Muslim only, so we should abide by that.

 Allaah knows best.