why does first mosit litmus paper red and then make it lose colour?
Not sure what the question is here. Are we talking about testing chlorine (or another halogen) gas with litmus?
The halogens are sometimes called acid gases as they react with the water in moist litmus paper to form an acid. This acid turns the litmus red initially. After a while the bleaching property of the chlorine comes into play and the red litmus slowly loses its colour.
Hope this helps.