What is the ruling on the Adhan that occurs before the time of Fajr, and is the prayer after it valid, knowing that the mosque delays establishing the prayer until the time it is presumed that the dawn (Fajr) has begun?

The call to prayer (adhan) before its prescribed time is invalid by scholarly consensus, and performing it is forbidden. Whoever calls the adhan before its time must repeat it when the time for prayer begins. The only exception to this is the first adhan for Fajr prayer, based on the Prophet's (peace be upon him) saying: "Indeed, Bilal calls the adhan at night, so eat and drink until Ibn Umm Maktum calls the adhan." The first adhan for Fajr does not suffice for the second. The adhan is not a condition for the validity of prayer. So, whoever prays within the time after an adhan that was called prematurely, their prayer is valid, but the mu'adhin (caller of adhan) is sinful. Whoever calls the adhan before Fajr, assuming it is the second adhan, is sinful because some people's prayer before its time results from his action. If the error is based on observing the dawn, then the mu'adhins should be advised and the matter presented to scholars for a change in the situation.