What is the ruling on fasting a complementary day for Ramadan if people differed on its fasting? And when should the fasting be, if it is valid?

If one breaks their fast for a day in Ramadan, they must make it up (perform *qada'*) before the next Ramadan. There is no specific day on which this *qada'* must be performed. If the variation in people's fasting is due to their country relying on the legitimate sighting of the crescent moon, and they fasted for 29 days, then their fast is valid, and doubt does not harm them. However, if they relied on astronomical calculations and their fasting was incomplete compared to the legitimate sighting, then they must fast the missing days.