Adding specific post category between posts in loop

You can use this as a start. This need to go into functions.php. You can use your normal loop in your template files, no need to change anything there. This will add a post from a category after post 3 and 6. Just remember to change the category name with the slug of your category.

function category_after_third_post( $post ) {
        global $wp_query;

        if ( $wp_query->post != $post )
            return;

        if ( 3 != $wp_query->current_post || 6 != $wp_query->current_post )
            return;

        $args = array(
        'category_name' => 'uit-die-koskas',
        'posts_per_page' => 1
        );

        $catquery = new WP_Query($args);

        if ( $catquery->have_posts() ) :

            while ( $catquery->have_posts() ) : $catquery->the_post();

                get_template_part( 'content', get_post_format() );

            endwhile;

        endif; 
    }

add_action( 'the_post', 'category_after_third_post' );

Alternatively, you can create a widget and add that after every 3rd post.

function cat_posts_sidebar() {
    register_sidebar( array(
        'name' => __( 'Sidebar for ads', 'my-theme' ),
        'id' => 'sidebar-10',
        'description' => __( 'Sidebar to display cat post', 'my-theme' ),
        'before_widget' => '<aside id="%1$s" class="widget %2$s">',
        'after_widget' => '</aside>',
        'before_title' => '<h3 class="widget-title">',
        'after_title' => '</h3>',
    ) );    
}
add_action( 'widgets_init', 'cat_posts_sidebar' );

Then modify the first function to this.

function category_after_third_post( $post ) {
        global $wp_query;

        if ( $wp_query->post != $post )
            return;

        if ( 3 != $wp_query->current_post || 6 != $wp_query->current_post )
            return;

        echo '<div class="after-post-widget widget-area">';
             dynamic_sidebar( 'sidebar-10' );
        echo '</div><!-- end .after-post-widget -->';
    }

add_action( 'the_post', 'category_after_third_post' );