One can easily use
CONVERT_TZ(your_timestamp_column_name, 'UTC', 'your_desired_timezone_name')
For example:
CONVERT_TZ(timeperiod, 'UTC', 'Asia/Karachi')
Plus this can also be used in WHERE statement and to compare timestamp i would use the following in Where clause:
WHERE CONVERT_TZ(timeperiod, 'UTC', '{$this->timezone}') NOT BETWEEN {$timeperiods['today_start']} AND {$timeperiods['today_end']}