Praise be to Allah.
The worshipper should carry on praying, and not repeat after the mu’adhdhin, because he is busy with his prayer. So if the mu’adhdhin gives the call to prayer whilst you are praying, you should complete your prayer and not repeat after the mu’adhdhin.
But if you were offering the obligatory prayer when you heard the adhan, and you realised that you were praying before the time for that prayer had begun, then you should not complete it, because the obligatory prayer cannot be offered until after its time has begun, and you should not have started praying until after you had ascertained that the time for the prayer had begun.
If a person is sick at home, for example, or he has a valid reason that is keeping him from praying with the Muslims in the mosque, such as fear or sickness, then he may pray after the time for the prayer has begun, even if the adhan has not been given yet, because the mu’adhdhin may delay the adhan and give the call a while after the time for the prayer has begun. So if the worshipper has ascertained that the time has begun, then he may offer his obligatory prayer, even if he has not heard the adhan, such as a sick person who is in a house that is far away from the mu’adhdhin, or one who it is in a state of fear, or a traveller who cannot hear the adhan. But the Sunnah in the case of the traveller is to give the adhan himself before praying, if he is certain that the time for the prayer has begun; he should recite the adhan, then the iqamah, and pray.
As for one who is in a city or town, he should not pray until after the time for the prayer has begun. Once the time has begun and he is certain of it, it becomes permissible for him to pray even if he has not heard the adhan.
Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him)
Fatawa Nur ‘ala ad-Darb (2/720)