Adding variable to user profile page in drupal 6
Use the hook_menu in your custom module and use MENU_LOCAL_TASK as the type, and the path in your custom module needs to start with user/    

function HOOK_menu() {
      $items['user/%user/yourpage'] = array(
        'title' =&gt; t('My Tab'),
        'type' =&gt; MENU_LOCAL_TASK,
        'page callback' =&gt; 'yourmodule_page', //your module page should be a function 
        //'page arguments'
      );
      return $items;
    }

function yourmodule_page()
{
   $uid = arg(1);
   $user = user_load($uid);
   //use user to get particular content belonging to them
   //return content
}