First of all, it should be stressed that a person who missed some days of fasting during Ramadan has to make up for those days after Ramadan before the following Ramadan. If he or she did not make up for those missed days and the next Ramadan comes, then, according to some scholars, he or she has to make up for those days after Ramadan in addition to an expiation which is the payment of fidyah.
Sheikh M. S. Al-Munajjid, a prominent Saudi Muslim lecturer and author, states:
If a person delays making up missed Ramadan fasts until the following Ramadan begins, and that was for a reason such as sickness, pregnancy or breastfeeding, the person does not have to do anything except the make up for the missed days. However, if there was no excuse, the person must make up for the missed days immediately, but there is a difference of opinion among scholars about whether or not he or she has to pay fidyah. The majority are of the view that the expiation must be made, and it is done by feeding one poor person for every day. The more correct view is that the expiation is not obligatory, but the one who makes it to be on the safe side has done well.
This expiation according to those who say that it is required, becomes obligatory upon that person as soon as the following Ramadan begins, and he may offer it at that time, or delay it until he makes up for the fasts, but it is better to hasten to do it so as to fulfill his obligation.
It says in Al-Mawsu`ah Al-Fiqhiyyah (28/76): “Making up for the missed Ramadan fasts may be done at any time but the majority of scholars limited it to a specific time frame within which they must be made up, which is before the following Ramadan begins. This is based on the words of `A’ishah (may Allah be pleased with her): “I would owe missed Ramadan fasts but I would not be able to make them up except in (the month of) Sha`ban, because of my duties towards the Prophet (peace and blessings be upon him).” This is similar to Prayer, which should not be delayed until the time for the next Prayer comes.
According to the majority of scholars, it is not permissible to delay making up for missed Ramadan fasts until the following Ramadan comes without an excuse, and that doing so incurs sin. This is also based on the hadith of `A’ishah. If a person delays doing so, he must offer the expiation: feeding one poor person for each day. This is based on a report narrated by Ibn `Abbas, Ibn `Umar and Abu Hurairah (may Allah be pleased with them) who said concerning the one who has to make up for a missed fast but does not do so until the following Ramadan: “He must make it up and feed one poor person for each day.”
This expiation is for the delaying. It is permissible to offer food before making up for the fast, at the same time, or afterwards. al-Mardawi Al-Hanbali (may Allah have mercy on him) said:
“He should offer food that is acceptable for expiation. It is permissible to give the food before making up for the fast, at the same time, or afterwards. Al-Majd – meaning Ibn Taymiyah, the grandfather of Shaykh Al-Islam Ibn Taymiyah – said that the best way is to give it beforehand, in his view, so as to hasten to do good and to rid oneself from the problem of postponing.”