new WP_Query with order args – no more distinction between categories

On the template driving your archive page, you can use the query_posts() function to adjust the main query (WordPress’ default main query, not your custom one).

query_posts( array(
    'orderby' => 'modified',
    'order' => 'ASC',
) );

Using the pre_get_posts action is the better method, though slightly more complex (untested, would go in theme’s functions.php or an mu-plugin):

add_action( 'pre_get_posts', static function ( $query ) {
    if ( ! $query->is_main_query() || ! $query->is_category() ) {

    $query->set( 'orderby', 'modified' );
    $query->set( 'order', 'ASC' );
} );