Turkey timezone problem

You should be able to install the tzdata in the F5, see this solution for CentOS information:

https://support.f5.com/kb/en-us/solutions/public/3000/600/sol3645.html

However, I don't think the system will use the daylight information. The Linux system handles one time, and TMM (F5 kernel) handles another time. I know this because there was bug in the past were the linux system was showing different time comparing with TMM.

Both times are based in UTC/GMT times. Most people don't care about the change to daylight, as that has no impact to the system tasks. The only thing you have take into account is when looking the logs timestamp.

NTP servers don't work with daylight.

If I understand correctly your question, you don't need to do any change and just use Turkey timezone as you don't have daylight. If you need to have the time adjusted for daylight, just use another country with that timezone in the F5 configuration. See the list here:

https://en.wikipedia.org/wiki/List_of_time_zones_by_country