Okay. I'm assuming you have a list of times that patients attended your ER
and that this list appears in column A, such as:

A
1 07:20
2 07:24
3 08:13
4 08:43

Highlight the entire list of data and name the range "PTTimes"
(Insert--Name--Define).

In cell B1, type this formula:

=COUNTIF(PTTimes,"="&TIME(7,0,0))-COUNTIF(PTTimes,"="&TIME(8,0,0))

This should return the correct count of patients attending between 7am and
8am.

Is it not doing that?