Sorry, but it looks as if you didn’t bother to look at the very beginning of the landing page. GanttProject is a desktop application. What sort of REST API do you expect? How can it be anything else than “on premise”?
Did you try to launch GanttProject at least once?
Sorry again, it is absolutely okay to ask for help with questions which have no obvious answers. But this questionnaire looks as if you’re trying to delegate your job to someone else.