Load twig templates from the lib directory of your module

FooController.php

<?php

namespace Drupal\module_name\Controller;

use Drupal\Core\Controller\ControllerInterface;
use Symfony\Component\DependencyInjection\ContainerInterface;
use Drupal\Core\Template\TwigEnvironment;

class FooController implements ControllerInterface {
  
	public function __construct(TwigEnvironment $twig, $twig_loader) {
	    $twig_loader->addpath(str_replace('Controller','View',__DIR__));

	    $this->twig = $twig;
	  }

	public static function create(ContainerInterface $container) {
		return new static(
				$container->get('twig'),
				$container->get('twig.loader')
				);
	}

	public function displayTwig(){
		return $this->twig->render('displayTwig.html.twig');
	}
}