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use \Bitrix\Main,
   \Bitrix\Disk;

/**
 * Gerenated url or empty string
 * @var string
 */
$url = '';

/**
 * Disk attached object id
 * @var integer 
 */
$attachId = 1;

/**
 * Short link author id
 *     by default - user who create public link
 *     for example - admin (ID:1)
 * @var integer
 */
$authorId = 1;

try
{
   if ( !Main\Loader::IncludeModule('disk') )
   {
      throw new \Exception("Disk module not included");
   }

   /**
    * @var Disk\AttachedObject
    */
   $attachObject = Disk\AttachedObject::loadById($attachId);

   if ( !($attachObject instanceof Disk\AttachedObject ) )
   {
      throw new \Exception("Attached object not loaded");
   }

   /**
    * @var Disk\File
    */
   $diskObject = $attachObject->getObject();

   if ( !($diskObject instanceof Disk\File ) )
   {
      throw new \Exception("Disk object not loaded");
   }

   $extLinks = $diskObject->getExternalLinks([
      'filter' => [
         'OBJECT_ID' => $diskObject->getId(),
         'CREATED_BY' => $authorId,
         'TYPE' => Disk\ExternalLink::TYPE_MANUAL,
         '=IS_EXPIRED' => false,
      ],
      'limit' => 1,
   ]);

   $extLink = array_pop($extLinks);

   if ( !$extLink )
   {
      $extLink = $diskObject->addExternalLink([
         'CREATED_BY' => $authorId,
         'TYPE' => Disk\ExternalLink::TYPE_MANUAL,
      ]);
   }

   if (!$extLink)
   {
      throw new \Exception("Can't create or find external link");   
   }

   $url = new Main\Web\Uri(
      Disk\Driver::getInstance()->getUrlManager()->getShortUrlExternalLink(
         [
            'hash' => $extLink->getHash(),
            'action' => 'default',
         ],
         true
      )
   );
}
catch ( \Exception $e )
{
   var_dump($e->getMessage());
}

/**
 * $url - instance of Bitrix\Main\Web\Uri object
 * if use strVal($url) - return absolute path, e.g. https://**.ru/~KpyTY
 * string(56) "/bitrix/tools/disk/uf.php?attachedId=1&action=show&ncc=1"
 */
echo "<pre>";
var_dump($url);
echo "</pre>";