بسم الله الرحمن الرحيم
If you are reciting the Holy Quran in the mosque at the time of Azan then it is allowed to continue and in case you are at your home then you should stop the recitation and reply Azan.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.