Can You Pray Witr during Adhan for Fajr?
Question

I wake up shortly before Fajr, and sometimes the Adhan for Fajr starts, and I have not completed Witr, or I am reciting Du`a. Should I prostrate or not recite Qunut?
Praise be to Allah.In the answer to question no. 46544  and 32577  we have explained that the time for Witr is from after `Isha’ prayer until dawn breaks. 
If the Mu’dhdhin (one who calls the Adhan) gives the Adhan for Fajr whilst you are praying Witr , then Shaykh Ibn Baz (may Allah have mercy on him) said:  
What is prescribed for every believing man and woman is to pray Witr every night , the time of which lasts from `Isha’ prayer until dawn breaks, because it is narrated by Al-Bukhari and Muslim from Ibn ‘Umar (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “The night prayers are two by two, then when you fear that dawn is about to break, pray one Rak`ah to make the number of Rak`ahs that you have prayed odd.” 
There are many Hadiths which speak of this. This indicates that Witr ends when dawn breaks. If a worshipper does not know when dawn breaks, he may rely on the Mu’dhdhin who is known to seek the correct time. When the Mu’dhdhin who is known to seek the correct time gives the Adhan, then the time for Witr has ended. But if he gives the Adhan before dawn then the time for Witr does not end when he gives the Adhan, and that does not mean that it has become prohibited for one who is fasting to eat and drink, or that the time for Fajr prayer has begun. 
From what we have mentioned, it is clear that the time for Witr ends with the first Adhan if the Mu’dhdhin is seeking the correct time of dawn for his Adhan. But if the Mu’dhdhin gives the Adhan when the Muslim is in the last Rak`ah, he should complete it because he cannot be certain that dawn has broken just from hearing the Adhan, and there is nothing wrong with that in sha Allah.” (Majmu` Fatawa Ibn Baz, 11/305) 
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) was asked about a man who is praying Witr and whilst he is praying the Mu’dhdhin gives the Adhan for Fajr prayer. Should he complete his prayer? 
He replied: “Yes, if the Adhan is given whilst he is praying Witr , he should complete his prayer and there is nothing wrong with that.” (Fatawa Ibn ‘Uthaymin, 14/115)
And Allah knows best.