How to have a different section for a special category of posts in landing page?

Question

It is possible, you will need to create another loop for that special category using WP_Query class. An example of a loop returning the “cats” category would be:

// WP_Query arguments
$args = array (
    'category_name'          => 'cats',
);

// The Query
$query = new WP_Query( $args );

// The Loop
if ( $query->have_posts() ) {
    while ( $query->have_posts() ) {
        $query->the_post();
        // do something
    }
} else {
    // no posts found
}

// Restore original Post Data
wp_reset_postdata();

Depending on the number of sections on your landing page, you will have multiple loops, but do not forget to reset each loop on the page.