prefix_the_posts.php

<?php

add_filter( 'the_posts', 'prefix_the_posts', 10, 2 );

/**
 * @param array    $posts
 * @param WP_Query $wp_query
 *
 * @return array
 */
function prefix_the_posts( $posts, $wp_query ) {
    if ( $wp_query->is_main_query() && ! $wp_query->is_paged() && $wp_query->is_category( 'no-cat' ) ) {
        $arr_posts = [];

        $posts_ads = get_posts( [
            'category_name' => 'ads',
            'order'         => 'ASC',
            'orderby'       => 'menu_order',
        ] );

        foreach ( $posts_ads as $post_ads ) {
            if ( $post_ads->menu_order > 0 ) {
                $post_ads->menu_order               = $post_ads->menu_order - 1;
                $arr_posts[ $post_ads->menu_order ] = $post_ads;
            }
        }

        foreach ( $posts as $post ) {
            prefix_add_post( $post, $arr_posts );
        }

        return $arr_posts;
    }

    return $posts;
}

/**
 * @param WP_Post $post
 * @param array   $arr_posts
 */
function prefix_add_post( $post, & $arr_posts ) {
    static $offset = 0;

    if ( isset( $arr_posts[ $offset ] ) ) {
        ++ $offset;
        prefix_add_post( $post, $arr_posts );
    } else {
        $arr_posts[ $offset ] = $post;
    }
}