Hi @Anonymous ,
Do you want to refresh the data source every minute for some time period after midnight?
I have made a test for your reference.
1. Create a flow.
utcNow()
addHours(startOfDay(utcNow()),6)

2. Create a App.
3. Add a Timer Control and apply the following formula on its OnTimerStart property as:
Set(var_status,flowname.Run().var_refresh)

4. Add a new Timer Control and apply the following formula on its OnTimerEnd property as:
If(var_status="true",Refresh(DataSource));Set(var_status,"false")

Best Regards,
Charlie Choi