What is incumbent upon a patient who underwent a kidney transplant and was prohibited by his doctor from fasting, knowing that he pays expiation for each day?

A trustworthy Muslim doctor must be consulted. If fasting delays recovery or exacerbates the illness, then fasting is not permissible. The patient must make up the days of Ramadan they missed after recovering, based on the Almighty's saying: "But whoever among you is ill or on a journey [during them] - then [he must make up] an equal number of other days." There is no fidyah (feeding of the poor) required for this.

However, if the illness is incurable, then one must feed a poor person for each day of Ramadan they missed, based on the Almighty's saying: "And upon those who are able [to fast, but with hardship] - a ransom [as substitute] of feeding a poor person." This verse has been interpreted as referring to the elderly who cannot fast or the ill whose recovery is not hoped for.