Using 'kMDItemContentModificationDate' in 'do Shell Script'
Came up with this solution with help of above script which works just fine:

set downloadPath to path to downloads folder from user domain as string
set posixPath to quoted form of POSIX path of downloadPath

--Date to search for:
set dateStart to text returned of (display dialog "Enter search date in form 'MM/DD/YYYY'" default answer "02/03/2015")
--date "Tuesday, February 3, 2015 12:00:00 AM"
set dateStart to date dateStart
--End date (Midnight on next day)
set dateEnd to (dateStart + 24 * 60 * 60 * 1)
--date "Wednesday, February 4, 2015 12:00:00 AM"

--Begin search to now in days (rounded)
set startRound to round ((current date) - dateStart) / 86400
--End search to now in days (rounded)
set endRound to round ((current date) - dateEnd) / 86400
--Search Item
set SearchItem to "."

set theFiles to (do shell script "mdfind -onlyin " &amp; posixPath &amp; " 'kMDItemDisplayName == \"*" &amp; SearchItem &amp; "*\"&amp;&amp; kMDItemContentModificationDate &gt;= $time.today(-" &amp; startRound &amp; ") &amp;&amp; kMDItemContentModificationDate &lt;= $time.today(-" &amp; endRound &amp; ")'")