We know when we say `midday’, we mean 12 o’clock in the afternoon. Since we are referring to a specific time in the afternoon, we should use `at’ and not `during’.
We should say, “They have wada and dosai” at midday. If you would like to use `during’, then use `middle’ rather than `midday’.
*The clerk told us that the forms would be distributed at midday. *You’d better take a cap. It gets really hot during the middle of the day.