How can I handle publication jealousy among peers in my research lab?

I share an office with several grad students in a similar situation of non-overlapping fields. The problem extended to the PhD students of the program in general.

Is it common for others who have experienced such behavior during their graduate studies? Or, is it a paranoia?

In my experience, it is completely normal, but as you say, not desirable. I have heard that programs with less pressure to publish experience it less. I remember learning that a Masters student had entered the PhD program with a publication and felt like I had been punched in the gut.

How to handle such uncomfortable feeling inside the lab and feel positive?

To echo some of the comments, a lot of it seems to boil down to openness and collaboration. Here are some options that have helped me and my fellow grad students reduce negativity and increase the quality of our research:

  1. Reading about the publishing process and ways to get better at it, like with How to Write a Lot.
  2. Start or join a weekly writing group with your lab mates to mutually support one another. For me, this was the game changer. We talk about the good and the bad, as @Stefan_W mentioned.
  3. Find a supportive community outside the lab where you can discuss your feelings. For example, in Barcelona, we have several city-wide communities of early career researchers from every discipline.
  4. Similar to Point 3, participate in the associations of your field. For example, I attend events for the British Academy of Management. Not only do they hold seminars for grad students, but they generally require me to bring a work in progress, which has a motivating effect.

At my university, we went so far as to start a student association. We hold regular social events, mock conferences, organize writing groups, and participate in community events. These have started us in the direction of a feeling of shared victory (instead of resentment) when one of us manages to publish, and of course it gives us a place to turn for support in the case of rejection. In the beginning there were just a few of us in a weekly writing group, but eventually we got more organized.