Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
You committed one of the gravest sins and violated the sanctity of the blessed month of Ramadan. You should sincerely repent to Allah, make up for the fast day you broke, and offer kaffarah (expiation) for breaking your fast.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states,
You ought to repent and expiate for the most heinous offence you have committed. It is a double offence: You violated the sanctity of the month through sexual intercourse; this itself is the most heinous offence; secondly, even more wicked is committing adultery.
You ought to fast sixty days for the fast you broke; if you cannot do so, you should feed sixty poor persons. On top of that, you should seek sincere repentance. Repentance is not simply saying, “I am sorry”; rather it cannot be complete unless you take immediate steps of expiation; these are the essential conditions for repentance:
First of all, no repentance is earnest unless you feel deep remorse over your actions.
Secondly, you need to refrain from the sin you are repenting from; in this involves cutting off all relations with the person and leaving the company or circumstances that caused you to slip up;
Thirdly, you need to resolve never to do it again.
This is to be followed up by engaging in good deeds as much as you can.
It behooves you to keep the company of the pious and God-fearing who can exercise a beneficial influence over you. You may do well to spend the days in reading the Qur’an and dhikr as much as possible and spend the nights as much as possible in the mosque attending prayers.
Allah Almighty knows best.