Get datetime between start and end datetime
Full overlap:

SELECT * 
FROM source
WHERE Start_Date &gt;= '2019-09-11 12:00.000' 
  AND End_Date &lt;= '2019-09-11 13:15.000'


Partial overlap (not adjacent only, for adjacents replace strong unequiations &gt; and &gt; with safe ones &gt;= and &lt;=):

SELECT * 
FROM source
WHERE End_Date &gt; '2019-09-11 12:00.000' 
  AND Start_Date &lt; '2019-09-11 13:15.000'


fiddle