Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If you do not have the means to offer fidyah, you don’t have the obligation. If your son or someone else volunteers to pay it on your behalf, they can do so with your consent.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
If you are suffering from a terminal illness, you must offer fidyah to a poor person every day of Ramadan if you can afford it.
Allah says, “As for those who can afford, they should expiate themselves by feeding a needy person.” (Al-Baqarah 2: 184)
Therefore, it is binding on you if you have the means; if you do not, then you don’t have the obligation to pay the fidyah. Allah says, “God does not burden any soul beyond its capacity. (Al-baqarah 2: 286)
However, if your son or someone else volunteers to pay it on your behalf, they can do so with your consent. Since it is an act of worship, you must have the intention.
Almighty Allah knows best.
Source: AsktheScholar.com