Fasting: Missed Fasts Due to an Excuse Continuing Until the Following Ramadan
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 1672
If due to illness one does not fast in the month of Ramadan and his illness continues until the month of Ramadan of the following year, it is not obligatory for him to make up the fasts he did not keep; and for each day he must give one mudd (approximately 750 grams) of food – i.e. wheat, barley, bread, and suchlike – to a poor person.[1] However, if one does not fast because of another legitimate excuse – for example, he was travelling – and his excuse remains valid until the following month of Ramadan, he must make up the fasts that he did not keep; and the obligatory precaution is that for each day, he must also give one mudd of food to a poor person.
-Ayatullah Sistani, Practical Laws of Islam, Fasting (Sawm)
This type of compensative payment is known as fidyah.