Is it obligatory to make up a fast on a day when one broke it, thinking that the time had begun based on a mistaken adhan, while a means of verifying the adhan of Makkah Al-Mukarramah was available?

One who breaks their fast in Ramadan (definition), thinking the sun has set, but it then becomes clear it has not, must make up that day. This is the view of the majority of scholars, including the four Imams. This is based on what Al-Bukhari narrated from Asma bint Abi Bakr (may Allah be pleased with her) that they broke their fast on a cloudy day, then the sun appeared. When Hisham was asked, "Were they commanded to make up the fast?" he replied, "There must be a making up." Further supporting this is what Malik narrated in Al-Muwatta from Umar ibn Al-Khattab (may Allah be pleased with him) that he broke his fast on a cloudy day, then the sun appeared. Umar said, "The matter is easy, and we have exercised our judgment." Malik said, "He means making up the fast, in our opinion."