Hearing the Adhan of Fajr while Having Intercourse
Question

What is the ruling if the adhan is given for Fajr when a man is having intercourse with his wife? Should he carry on until he reaches climax, or should he stop as soon as he hears the adhan? Please advise us, may Allah reward you with good.
Praise be to Allah.Having intercourse when the time of Fajr comes
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 (kaffarah). 
The kaffarah 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. But this has to do with the onset of dawn. 
Hearing the adhan of Fajr while having intercourse
With regard to the adhan of the muadhdhin, if the muadhdhin gives the adhan at the time when dawn comes, then he must stop having intercourse as soon as he hears the adhan . If he does not do that, then he must make up the fast as well as offering the expiation, as stated above. 
If the muadhdhin gives the adhan before dawn comes, as some muadhdhins 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 ‘Uthaymin (may Allah have mercy on him) was asked the following question: 
If a fasting person drinks something after he hears the adhan for Fajr, is his fast valid?  
He replied: 
“If the fasting person drinks something after he hears the adhan for Fajr , if the muadhdhin gives the adhan 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 adhan before he sees the dawn, then there is nothing wrong with eating and drinking until the dawn is seen, because Allah 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).” [al-Baqarah 2:187]
And the Prophet (peace and blessings of Allah be upon him) said: “Bilal gives the adhan at night, so eat and drink until you hear the adhan of Ibn Umm Maktum, for he does not give the adhan until dawn comes.” 
Hence the muadhdhins should try not to give the adhan 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 Allah has permitted, or lead them to perform Fajr prayer before the time for it has come. This is a very serious matter indeed.” (Fatawa Islamiyyah, 1/122) 
For more, please see these answers: 38287 , 1051 , 279524 , and 21806 .
And Allah knows best.