What is the ruling regarding someone who ate, drank, and had intercourse with his wife after the dawn (Fajr) adhan, being ignorant of its prohibition, and relying on his incorrect understanding of the verse: "until the white thread of dawn becomes distinct to you from the black thread [of night]"?

Abstaining from things that invalidate the fast begins at the dawn. So, whoever eats or drinks after the Fajr adhan, and the adhan was after the dawn, their fast is invalidated, and they must make up for it. If the adhan was before dawn, their fast is not invalidated. And whoever hears the Fajr adhan while engaging in sexual intercourse, and the adhan was after dawn and they continued the intercourse, their fast is invalidated, and they must make up for it and offer the major expiation, unless they were ignorant of the ruling, in which case they only need to make up for it.