Here's an attempt.
I created a field called "Quarter_Interest" that creates the date of the quarter you are interested in. This is made from two parameters you have to choose from (Quarter and Year).
Then the calculated field "In_Quarter" has some logic and date parsing to determine if the incident was in that quarter ("Y" or "N").
See the attached workbook. Please check the logic and various situations to make sure it works correctly. (I populated a bunch of randomly generated dates in there to make this.)
quarter count.twbx 67.6 KB