If he hears the adhaan for Fajr whilst he is having intercourse with his wife
If dawn has come and he is having intercourse with his wife, then he has to stop having intercourse at once, and his fast is valid and he does not have to do anything. It is not permissible for him to carry on having intercourse after dawn has come. If he does that then his fast is invalid and he has to make up the fast and also offer the expiation (kafaarah).
The kafaarah is to free a slave. If that is not possible then he must fast for two consecutive months. If he is unable to do that then he must feed sixty poor persons. See question no. 1672.
But this has to do with the onset of dawn. With regard to the adhaan of the muezzin:
If the muezzin gives the adhaan at the time when dawn comes, then he must stop having intercourse as soon as he hears the adhaan. If he does not do that then he must make up the fast as well as offering the expiation, as stated above.
If the muezzin gives the adhaan before dawn comes, as some muezzins mistakenly do so that they will be on the safe side for fasting, as they claim, then it is permissible to continue having intercourse until he is certain that dawn has come.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked the following question:
If a fasting person drinks something after he hears the adhaan for Fajr, is his fast valid?
If the fasting person drinks something after he hears the adhan for Fajr, if the muezzin gives the adhaan after he is certain that dawn has come, then it is not permissible for the fasting person to eat or drink anything after that. If he gives the adhaan before he sees the dawn, then there is nothing wrong with eating and drinking until the dawn is seen, because Allaah says (interpretation of the meaning):
“and eat and drink until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night)”
And the Prophet (peace and blessings of Allaah be upon him) said: “Bilaal gives the adhaan at night, so eat and drink until you hear the adhaan of Ibn Umm Maktoom, for he does not give the adhaan until dawn comes.”
Hence the muezzins should try not to give the adhaan for Fajr until they see the dawn or they are certain that it has come according to correct clocks, so that they do not cheat the people and forbid for them something that Allaah has permitted, or lead them to perform Fajr prayer before the time for it has come. This is a very serious matter indeed.
Fataawa Islamiyyah, 1/122
And Allaah knows best.