prev & next_posts_link not appearing in custom index page template

I’m making my theme for WordPress, and I created a special index-with-sidebar.php custom page template and placed the Loop inside it. In WP Admin I’ve created a new page and set the front page to Index with Sidebar in the Customizer. In the footer.php file I have a prev_post_link and next_post_link which seems to be appearing in index.php, and not in the index-with-sidebar.php.

Should I replace the prev_post_link and next_post_link with sth other, or do I making something wrong? Any help appreciated!