Source: Fatawa ‘Ulama-e-Hadith, Kitab al-Salah, Volume 1, Page 174
❀ Question
There is a difference of opinion regarding the timing between the Adhan and congregation for Fajr prayer. One group offers the two Sunnah units immediately after the Adhan and proceeds with the congregational prayer right away. Another group waits for a while and offers the prayer in between the Adhan and sunrise. The question is: Which group is correct? What should be the correct time for Adhan, and how long should the wait be to maintain unity?
❀ Answer
The Adhan for Fajr should be given immediately after the appearance of true dawn (Subh Sadiq). However, it is preferable to wait for a short while before holding the congregational prayer.
The Prophet ﷺ used to wait long enough after the Adhan so that someone who was asleep could wake up, perform ablution, and join the congregation.
◈ Reference
Fatawa Thanaiyyah, Volume 1, Page 335