At the company where I work, we use OTRS to schedule tickets and such. But the web interface is not very intuitive and easy to use, particularly on mobile...
Is it possible to create my own mobile version of OTRS? I mean, I can create a website that is mobile optimised and easy to use, but is there an API to communicate with OTRS?
I've only seen simple scripts to create tickets via soap or rest interface, I need to create a ticket, show a list of the user tickets and close them, postpone them...
It is very much possible, since the OTRS is Open Source and you can basically do whatever you want with it. You might however underestimate the scope of the task you're talking about. I once thought about doing something like this too, but when you look at the functionality the OTRS is providing in the background and all the little details you need for a working interface you will probably come to the conclusion that it requires a LOT of work.
You could use the Generic Interface to create a Webservice that enables you to access ticket information etc. and build your own Frontend that utilizes the Webservice. I can tell you from experience that there is lots of functionality you need to add to the webservice to create a decent API for your Frontend, because the Information the Generic Interface offers by default is very limited.
Since OTRS Version 5 the software includes an interface with responsive design in order to make it better suited for mobile use. Depending on the version you are currently using you might consider upgrading to it. If you want to check it out first you can have a look at the online-demo they feature on their website: https://www.otrs.com/otrs-demo-trial/
If you like the concept of the OTRS but the interface makes it difficult to use for you, the founder of the OTRS released a different kind of ticket system called Zammad. You might want to check it out, it's interface is aimed at being more intuitive.
tl;dr
Yes, it's certainly possible - the OTRS is an open system, but very difficult and probably not worth the effort.