您在此行中有错误：

$sth->bindParam('refone', $refone);

应该是

$sth->bindParam(':refone', $refone);

带有:
另外，我会将WHERE子句放在条件语句中：

public function get_all($refone,$per_page,$page_offset) {

    if(!empty($refone)){
        $refone_condition = ' WHERE rq_detail LIKE :refone ';
        $refone = "%".$refone."%";
    } else {
        $refone_condition = ' ';
    }

    $query = "SELECT * FROM ". self::$table_name . $refone_condition;
    $query .= " ORDER BY rq_created DESC";
    $query .= " LIMIT " . intval($per_page);
    $query .= " OFFSET " . intval($page_offset);
    $sth = $this->conn->prepare($query);

    if(!empty($refone)){
      $sth->bindParam(':refone', $refone);
    }

    $sth->execute();
    return $row = $sth -> fetchAll();
}

注意，我还使用intval（）清理了$per_page和$page_offset，您也可以像使用：refone那样绑定它们，这样prepared语句就会负责清理它们。
更通用的代码也是如此：

public function get_all($refone = NULL, $per_page = NULL, $page_offset = NULL) {

    $args = array();
    $conditions = array();
    $offset_limit_clause = '';

    if(!is_null($refone)){
        $conditions[] = ' rq_detail LIKE ? ';
        $args[] = "%".$refone."%";
    }

    if(!is_null($page_offset)){
        $offset_limit_clause = ' OFFSET ? ';
        $args[] = intval(($page_offset-1) * $per_page); // offset is expressed in pages
                                                      // must convert to records
        if(empty($per_page)) $per_page = 30; // $per_page cannot be 0 if $page_offset > 1
    }

    if(!is_null($per_page)){
        $offset_limit_clause .= ' LIMIT ? ';
        $args[] = $per_page;
    }

    $query = "SELECT * FROM " . self::$table_name . 
    (count($conditions)?" WHERE ":"") . implode(" AND ", $conditions) .
    " ORDER BY rq_created DESC " . $offset_limit_clause;

    $sth = $this->conn->prepare($query);

    $sth->execute($args);
    return $row = $sth -> fetchAll();
}

最后但并非最不重要的一点是，您可以为函数中的参数设置默认值：

public function get_all($refone = NULL, $per_page = 30, $page_offset = 0) {

如果您不传递任何内容，则将使用默认值，但如果您传递NULL或0或“"等空/错误值，则将接收这些值，因此我认为这不是您在这里要查找的内容。

试试这个...

public function get_all($refone,$per_page,$page_offset) {
    $query = "SELECT * FROM ". self::$table_name . " WHERE rq_detail LIKE :refone";
    $query .= " ORDER BY rq_created DESC";
    $query .= " LIMIT $per_page";
    $query .= " OFFSET $page_offset";
    $sth = $this->conn->prepare($query);
    if(empty($refone)){
        $refone = '';
    } else {
        $refone = "%".$refone."%";
    }

    $sth->bindParam(':refone', $refone);
    $sth->execute();
    return $row = $sth -> fetchAll();
}

您忘记了这个。更正/添加这个...

$refone = '$';