Twenty Fifteen: Adjacent posts by menu_order [duplicate]

EDIT

According to the OP, this question/answers solved the issue

ORIGINAL ANSWER

the_post_navigation(), right down to its very core, uses get_adjacent_post() to return and display the next and previous post to the currently viewed post.

By default, these adjacent posts are returned by post date. We can alter that by filtering the relevant ORDERBY clause of the SQL query. This filter we will be using is the get_{$adjacent}_post_sort filter where the dynamic {$adjacent} part refers to next or previous link.

Here is how the filter looks like:

apply_filters( "get_{$adjacent}_post_sort", "ORDER BY p.post_date $order LIMIT 1", $post );

So, in a custom plugin or your theme’s function file, we can do the following: (NOTE: This is untested, and we will only add our filter when a certain post type is displayed)

add_filter( 'get_next_post_sort',     'wpse_220361_adjacent_post_sort', 11, 2 );
add_filter( 'get_previous_post_sort', 'wpse_220361_adjacent_post_sort', 11, 2 );
function wpse_220361_adjacent_post_sort ( $orderby, $post )
{
    // Make sure we are on our desired post type
    if ( 'MY_CUSTOM_POST_TYPE_SLUG' !== $post->post_type )
        return $orderby;

    // We are on the desired post type, lets alter the SQL
    $orderby = str_replace( 'post_date', 'menu_order', $orderby );

    return $orderby;
}