Should I put on my CV a postdoc which I am going to quit? I am currently doing a postdoc but I am looking for something else as the position turned out to be completely different with respect to the job description.
I have been in this postdoc for 4 months and I will leave as soon as I find another job. Should I include this short period on my CV?
I am applying to research positions both in academia and industry.
You absolutely should put this postdoc on your resume. It is where you are currently working, and given the times you have no good idea just how much longer you will be working there. The fact that you have a position is a positive indicator.
Now, this will raise some questions in the hiring process at other institutions, but a 4+ month hiatus would be similarly questioned. And you have good explanations as to why you want to move on. Note that in 6 or so months nobody is really going to be worried about it, since postdocs are limited term in the first place.
As an aside, I would say that you should perform more due diligence in selecting your next position, since there seems to have been some miscommunication. And, no, having a postdoc at a national lab is not generally seen as a negative either in industry or academia.