function adjacent_post_by_category( $category, $direction, $content ) {

    // Info
    $postIDs = array();
    $currentPost = get_the_ID();

    // Get posts based on category
    $postArray = get_posts( array(

        'category' => $category,
        'orderby'=>'post_date',
        'order'=> 'DESC'

    ) );

    // Get post IDs
    foreach ( $postArray as $thepost ):

        $postIDs[] = $thepost->ID;

    endforeach;

    // Get prev and next post ID
    $currentIndex = array_search( $currentPost, $postIDs );
    $prevID = $postIDs[ $currentIndex - 1 ];
    $nextID = $postIDs[ $currentIndex + 1 ];

    // Return information
    if( $direction == 'next' AND $nextID ):

        return '<a rel="next" href="' . get_permalink( $nextID ) . '">' . $content . '</a>';

    elseif( $direction == 'prev' AND $prevID ):

        return '<a rel="prev" href="' . get_permalink( $prevID ) . '">' . $content . '</a>';

    else:

        return false;

    endif;

}

—————-

And this as your prev/next links (function parameters are examples):

<?php echo adjacent_post_by_category( 10, 'prev', 'Show previous post' ); ?>

<?php echo adjacent_post_by_category( 10, 'next', 'Show next post' ); ?>

—————-

Regards
Louis
https://wemanageyoursite.com/