trying to get property
Check the manual for mysql_fetch_object(). It returns an object, not an array of objects.
I'm guessing you want something like this
$results = mysql_query("SELECT * FROM sidemenu WHERE `menu_id`='".$menu."' ORDER BY `id` ASC LIMIT 1", $con);
$sidemenus = array();
while ($sidemenu = mysql_fetch_object($results)) {
$sidemenus[] = $sidemenu;
}