I want to display custom error messages below that text field in
comments form. Currently it displays all error messages above the page which is not acceptable.
You need go to your theme's template folder and edit page.tpl.php'
<?php print $messages; ?> and move it below
<?php print render($page['content']); ?>
Thanks for the note @Kevin. If you wish, you can add if statements around the
<?php print $messages; ?> that check the page url and/or content type if you need to have them appear below only for certain pages.