What is the ruling on the pre-dawn Fajr Adhan that is called a quarter of an hour before its time, and is it obligatory to stop it if it is not possible to delay it to the correct time?

If the adopted calendar used to determine the time of Fajr has been approved by trustworthy scholars, then no attention should be paid to doubts about it, and the adhan (definition) should continue to be called based on it. This is unless the one raising doubts is a scholar himself, in which case verification and investigation are necessary. However, if the calendar has not been supervised by trustworthy scholars, or its source is unknown, then it should not be relied upon. In such a case, it is obligatory to investigate and ascertain the entry of true Fajr before the adhan, so that no one prays before the time has commenced.