How can i make my own ticketing system?
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how can i make my own ticketing system? (like otrs,rt,itop)
is it possible with API? - 
Short answer: Yes.
Honestly, I have no idea why you would like to re-invent the wheel

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The esxisting implementations use the API to access i-doit objects and either store them in the ticket system or store a link to them.
The ticket category within i-doit can be extended, but you have to write your own code. If you are interested in details, feel free to contcat me via PM.