how can i make this type of notification hidden or make the post to not show in my "show new replies to your posts" section,
I am sorry to say, but I do not think it is possible to make this type of notification hidden. The whole purpose of this feature is to keep you updated on new activity related to your posts.
I participated first time in bounty campaign but how can i get rid of this unwanted notification.
If you do not want to go through and read every single thread, you can simply click on
"mark all messages as read" which will clear the list. At least until the next reply in one of those threads.