Does expiation have to be offered for having intercourse when making up a missed Ramadaan fast?

Making up missed Ramadaan fasts is obligatory, and it is not
permissible to break such a fast except in case of necessity. Once a person
starts to observe a fast to make up a fast he missed, he is obliged to
complete it, and it is not permissible for him to break it except for a
legitimate shar’i excuse. 

It was narrated that Umm Haani’ (may Allaah be pleased with
her) said: “O Messenger of Allaah, I broke my fast when I was fasting.” He
said to her: “Were you making up a missed fast?” She said: “No.” He said:
“Then it does not matter if it was a voluntary fast.” Narrated by Abu
Dawood, no. 2456; classed as saheeh by al-Albaani. This indicates that it
would matter if she broke her fast when observing an obligatory fast. What
is meant by “it would matter” is that it would be a sin. 

With regard to what
happened in your case, the expiation of intercourse is only required if what
is broken is a fast in Ramadaan itself. Based on this, you do not have to do
anything except make that day up again, as well as repent to Allaah and
resolve not to do such a thing again. 

Ibn Rushd said: The majority are agreed that no expiation is
required for deliberately breaking a fast observed to make up a missed
Ramadaan fast, because it does not come under the same category with regard
to sanctity of time, i.e., Ramadaan. 

Bidaayah al-Mujtahid, 2/80. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was
asked about a woman who broke a fast she was observing to make up for a
missed Ramadaan fast, to make her guests feel comfortable. He replied: If
she was making up a missed obligatory fast, such as making up a day of
Ramadaan, then it is not permissible for anyone to break such a fast except
in cases of necessity. With regard to breaking the fast because of the
arrival of guests, this is haraam and is not permitted, because the basic
principle in sharee’ah is that “Everyone who starts an obligatory duty is
required to complete it, unless he has a legitimate shar’i excuse.”  But if
he is making up a voluntary fast then he does not have to complete it,
because it is not obligatory. 

Based on this, if a person is observing a naafil
(supererogatory) fast and something happens that means he has to break his
fast, he may do so. This is what was narrated from the Prophet  (peace
and blessings of Allaah be upon him), that he came to the Mother of the
Believers ‘Aa’ishah  (may Allaah be pleased with her) and said: “Do you have
anything (to eat)?” She said: “We have been given some hays (a kind
of meal).” He said: “Show it to me, for I started fasting this morning.” And
he (peace and blessings of Allaah be upon him) ate some of it. This has
to do with a naafil fast, not one which is obligatory. 

Majmoo’ al-Fataawa, 20.