wpdb query problem to access previous 3 days posts

You are asking for the last three posts ordered by post date, not for the posts from the last three days– ORDER BY post_date DESC LIMIT 3. post_date has a time component to it. It is not just marked with a date. Even so, that LIMIT would restrict the query to last three in the list, not all of the posts that are more recent than three days.

What you need is something like this:

SELECT post_title 
FROM $wpdb->posts 
WHERE post_status="publish" 
AND post_author = 2 
AND post_date > DATE_SUB(CURDATE(), INTERVAL 3 day)
ORDER BY post_date DESC

See the following for other options and caveats: https://wordpress.stackexchange.com/a/96562/21376

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