previous and next post of same category on singlepost.php

I would not use get_posts() to setup my loop on the single.php page. I would just use the normal proper loop. Please check out this page in the codex about Theme Development

Here is an example of a single.php that will work as expected

<div id="primary" class="content-area">
    <div id="content" class="site-content" role="main">
        <?php
            // Start the Loop.
            while ( have_posts() ) : the_post(); ?>

        <?php
                get_template_part( 'content', get_post_format() );

                // Previous/next post navigation.
                previous_post_link( '%link', 'Prev post in category', true );
                next_post_link( '%link', 'Next post in category', true );

                // If comments are open or we have at least one comment, load up the comment template.
                if ( comments_open() || get_comments_number() ) {
                    comments_template();
                }
            endwhile;
        ?>
    </div><!-- #content -->
</div><!-- #primary -->

As pointed out in the other answer, go and have a read on how to use the next_post_link and the previous_post_link