What is the ruling on the fast of one who drank water after the second Adhan, based on several popular sayings, and does the ruling differ if the cup was in his hand or in front of him? And what is the extent of validity of these sayings?

Legally mandated fasting is abstaining from things that break the fast from the emergence of the second dawn (the true dawn) until sunset. If the muezzin calls the adhan for the emergence of dawn, then one must stop eating and drinking as soon as the adhan is heard. However, if the muezzin calls the adhan a little before the time, there is no harm in eating and drinking during the adhan. Fasting must be made up if the muezzin adheres strictly to the time, but there is nothing upon you if he calls the adhan a little before the time.