Wordpress single page template, custom post type, pagination orderby title - alphabetical order

Try this Solution:

For this you should create custom shortcodes. Please add this code in your theme’s or child theme’s functions.php file:

add_shortcode( 'next_post', 'next_shortcode' );
function next_shortcode($atts) {
    global $post;
    ob_start();
    next_post_link( '<span class="nav-next">%link : Next ></span>', '%title' );
    $result = ob_get_contents();
    ob_end_clean();
    return $result;
}   
add_shortcode( 'prev_post', 'prev_shortcode' );
function prev_shortcode($atts) {
    global $post;
    ob_start();
    previous_post_link( '<span class="nav-previous">< Previous : %link</span>', '%title' );
    $result = ob_get_contents();
    ob_end_clean();
    return $result;
}
function my_custom_adjacent_post_where($sql) {
    if ( !is_main_query() || !is_singular() || 'your-custom-post-type-slug' != get_post_type() )
        return $sql;
    $the_post = get_post( get_the_ID() );
    $patterns = array();
    $patterns[] = '/post_date/';
    $patterns[] = '/\'[0-9]{4}-[0-9]{2}-[0-9]{2} [0-9]{2}:[0-9]{2}:[0-9]{2}\"https://wordpress.stackexchange.com/";
    $replacements = array();
    $replacements[] = 'post_title';
    $replacements[] = $the_post->post_title;
    return preg_replace( $patterns, $replacements, $sql );
}
add_filter( 'get_next_post_where', 'my_custom_adjacent_post_where' );
add_filter( 'get_previous_post_where', 'my_custom_adjacent_post_where' );
function my_custom_adjacent_post_sort($sql) {
    if ( !is_main_query() || !is_singular() || 'your-custom-post-type-slug' != get_post_type() )
        return $sql;
    $pattern = '/post_date/';
    $replacement="post_title";
    return preg_replace( $pattern, $replacement, $sql );
}
add_filter( 'get_next_post_sort', 'my_custom_adjacent_post_sort' );
add_filter( 'get_previous_post_sort', 'my_custom_adjacent_post_sort' );

Whereas ‘your-custom-post-type-slug’ is your custom post type slug, that you need to replace in the above code.

Then, add this shortcode in your Content Template to display Previous and Next post links:

[prev_post] | [next_post]

Expected Output:

< Previous : Post Name | Post Name : Next >

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