if (!$a) {
  return ['#markup' => 'no'];
}

return new TrustedRedirectResponse($url);

public function mycontroller() {

  Drupal::service('page_cache_kill_switch')->trigger();

  if (!$a) {
    return [
      '#markup' => 'no',
      '#cache' => ['max-age' => 0],
    ];
  }

  return (new TrustedRedirectResponse($url))
    ->addCacheableDependency((new CacheableMetadata())->setCacheMaxAge(0));
}

my_awesome_module.do
  path: '/do-awesome'
  defaults:
    _controller: 'Drupalmy_awesome_moduleControllerMyAwesomeModuleController::doAwesome'
  options:
    no_cache: 'TRUE'