JetPack has a great Related Posts module, here’s how to move it further down the page below posts meta info or anywhere else you like by using a shortcode provided by JetPack.
In Genesis Themes for instance, it positions itself in the genesis_entry_content hook at the bottom. Lets say you wanted this below the post meta category information.
Well, JetPack has a shortcode that you can use to position the related posts where ever you like.
So when the above snippet is added to functions.php the default position is removed in the first function and in the second function the JetPack shortcode is used to reposition it using the genesis_entry_footerhook at a lower priority.
For a non-Genesis theme you would just add the shortcode to your PHP template files where you want the related posts to appear at a different position.
<?php echo do_shortcode([jetpack-related-posts]); ?>