Should I mention while applying to another PHD program that I have resigned from another one As you may know my story, I have been forced to leave after first year of PhD, now I am applying to positions and I have been rejected before which I think because I told them what happened to me. 

I would like to know what I can do and how I can add to my CV as it seems a problem.
Reading through some of the previous posts the OP has posted in regards to leaving a PhD program, it seems that the main issue is that the assigned advisor was perhaps combative and difficult to work with. I will proceed with this being the assumed reason for leaving the previous PhD program. 

First of all, it would be overall wise to briefly mention in an application that you were a former PhD student elsewhere. Omitting any mention of having been in a previous program will likely come back to haunt you. Thus, the question is not so much if you should disclose having been in a previous program, but how you disclose it. 

Stick to the facts, not ad hominem arguments or accusations. Universities will usually avoid applicants who bad mouth their previous program/advisor. Even if your previous program caused major issues for you personally, you never know what buddies your former program may have at other schools. 

I would simply indicate which classes you took, the grades you received, the research you performed. If you are able to attach indications of strong and positive work during your first year as a PhD student, this can certainly bolster your application. Obtaining a letter of recommendation from someone in your former PhD program could also be a strengthening point of your application.

All of this being said, you will need to be prepared to answer the question as to why you left your previous program. My advice in that regard is to pivot this question into answering why you want to join the program you are applying to. Be ready to be very specific. Mention specific professors and what you like about their work (which means you need to actually know about their work). Insofar as is possible, pivot everything to speaking of future positive work, not previous negative experiences and shortcomings.