Featured Category or Special Category in WordPress

You can do this by using the pre_get_posts filter, which allows you to change they query before it is executed. In this way you can add Cat A to any request for categories. Like this:

add_filter ('pre_get_posts', 'wpse380282_add_cat_a');
function wpse380282_add_cat_a ($query) {
  // do this only on the front end for the main query if it is a category archive
  if ( !is_admin() && $query->is_main_query() && is_category() ) {
    // get the ID for Cat A
    $cat_id = get_cat_ID ('Cat A');
    // get category of the query (returns an array of current categories)
    $cats = $query->get( 'cat' );
    // add Cat A to the array of current categories
    $cats[] = $cat_id;
    // set the category query to the expanded array
    $query->set( 'cat', $cats );
    }
  }