is it possible to write server side extension for RQM?

Accepted answer

As far as I can tell, RQM (and DoorsNext) does not provide an SDK and don't allow server side extensions because of that.
Comments

Is there any way to develop widgets for RQM? I would like to use that as a workaround for the functionality required

Widgets will be on the client side. Is it what you try to use? If so, consider the OSLC or REST API.

ETM/RQM does not provide an SDK, so there is no official way to develop server extensions for ETM/RQM.