If a man or woman breaks his/her fast in Ramadan due to a valid excuse – such as travel, illness, or menstruation, and later, outside of Ramadan, has spousal intercourse during the day when he/she was making up the Ramadan fast, is expiation required?

Whoever has spousal intercourse intentionally while making up a Ramadan fast:
Must make up the day.
Does not have to offer expiation; this is by agreement of the four main schools of thought. This is due to the absence of the sanctity of Ramadan itself and because expiation is specifically required when intercourse happens in Ramadan. Ibn Qudamah said, “And expiation is not required for one who breaks his/her fast outside of Ramadan according to the majority of Muslim jurists.”

There is a difference between ignorance of the transgression and ignorance of the consequential requirements. We understand this difference through the hadith of the companion who had intercourse with his wife during the day in Ramadan. He knew he had transgressed, however, he asked the Prophet (pbuh) what the expiation is for his wrong-doing.

Imam al-Nawawi said, “If the fasting person eats or drinks or has spousal intercourse out of ignorance of its prohibition and is in an environment that is predominantly non-Muslim which would make it easy for him to forget that he is fasting, then his fast would remain valid. However, if one is amongst Muslims in such a way that he is always surrounded by reminders of fasting and Ramadan rulings, then his fast has been broken due to his shortcoming.”