You will need to change the timezone on a job-by-job basis.
The TZ line should not be a line on its own in crontab, but it can be part of a normal line in crontab or be inside a script.
The syntax you show for TZ is incorrect.
What do you get in a normal interactive session for:
echo "${TZ}"
What Operating System and version are you running?
What Shell are you running?
Is your server clock set in UTC with default timezone in /etc/TIMEZONE ?
It is often easier to use the cron on a server which runs in the target timezone to trigger jobs on the server which is in a different timezone.