How to display entries relevent to date assigned
Assuming your date/time field is called dateField, and your entries channel is events.

You want to fetch just the entries that have dates in that month. You can do that like this:

If you know the year and the month, the start of the month is (~ is the twig string concatination operator):

{% set startDate = year~'-'~month~'-01' %}


And the start of the next month is:

{% set endDate = startDate|date_modify('+1 month')|date('Y-m-d') %}


We use twig's date_modify filter to get the start of the next month, and then twig's date filter to convert that to a string.

Now you can fetch the entries for the month. You want ones where the dateField is on or after startDate and before endDate.

{% set monthEvents = craft.entries
  .section('events')
  .dateField(['and', '&gt;= '~startDate, '&lt; '~endDate])
%}