Ask them (O Muhammad) of the township that was by the sea, how they did break the Sabbath, how their big fish came unto them visibly upon their Sabbath day and on a day when they did not keep Sabbath came they not unto them. Thus did We try them for that they were evil-livers.
Times are computed by method; your mosque's timetable governs the adhan. Every text carries its source and grade. Nothing here is a fatwa, a prediction, or a substitute for a doctor: your own scholar decides what is contested, and the tradition itself says the practice is alongside treatment, never instead of it.