Thank you Lucy. If I wanted to refer following day of 6th, which one would be correct?
"aftermath", "afterwards" or "later than"

You could say:
"The device will be shut down if the invoice is paid later than 6th day of the following month."
or
"If the invoice is not paid before of 6th day of the following month, the device will be shut down afterwards."
The first sentence is more natural though :)

Aftermath is a little different - it's usually used for talking about the period that follows an unpleasant event or accident.
"In the aftermath of the earthquake, there were a lot of damaged buildings"
"His divorce was the aftermath of his affair.

Thanks a lot Lucy. You are really helpful :)