Alter Reset Password Link When a user resets his password he/she gets an email with a link which adds a message to the website and a hyperlink which it redirects him to the /user/[uid]/edit?token=... page. 

How can i alter this link ?
I would prefer mail a new link to user rather than altering the current link.

Use Tokens API to create user wise links.

function MYMODULE_token_info() {
  $info['tokens']['user']['passresetlink'] = array(
    'name' =&gt; t('Password Reset link 2'),
    'description' =&gt; t("Password Reset link 2"),
  );
  return $info;
}


and 

function services_chat_tokens($type, $tokens, array $data = array(), array $options = array()) {
  $replacements = array();
  if ($type == 'user' &amp;&amp; !empty($data['user'])) {
    $user = $data['user'];
    foreach ($tokens as $name =&gt; $original) {
      switch ($name) {
        case 'passresetlink':
          //$user = user_load($node-&gt;uid);
          //$newlink = make your link here.
          $replacements[$original] = $newlink;
        break;
      }
    }
  }

  return $replacements;
}