What is the expiation for having sexual intercourse deliberately thinking that time of breaking the fast was due after hearing the Athaan of Maghrib from a remote Masjid (Mosque)?

All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

As long as intercourse took place after hearing the Athaan, there would be no blame on them. They are not required to make expiation. If one later discovered that the sun had not set and that the caller announced the Athaan by mistake, there would still be no expiation on them because they thought that the night had come and the day had elapsed. They are only required to make up for that day because Allaah The Almighty forgave what His slaves commit by mistake or out of forgetfulness. An-Nawawi said that the man who had sexual intercourse [in a day in Ramadan] thinking that the sun has set or the dawn did not break and later discovered otherwise would only make up for that fast (without any expiation). This is the opinion of Abu Haneefah, Maalik, Ahmad, Abu Thawr and the majority of scholars.

Therefore, the preponderant opinion is that there no expiation is required from them, but they are still required to make up for that day if they realized that they were mistaken about the setting of the sun. If there was not a mistake and the sun had really set then no making up or expiation will be due on them.

And Allaah Knows best.