I had set expired date of a page in cms and when it expired i think this page shouldn't show in my front end page search bar.
Well, it depends on how you have implemented the search. If you don't want to include expired content in the search you need to filter those out. If you're using a typed search you can see here how to filter here https://world.episerver.com/documentation/developer-guides/find/Integration/episerver-cms-7-5-with-updates/Filters/.
@ash this looks like the same issue you raised in this previous post last week. https://world.episerver.com/forum/developer-forum/EPiServer-Search/Thread-Container/2019/9/expired-pages-are-still-appearing-in-the-search-bar-at-the-front-end/
If so we should try to resolve the issue in the previous thread, rather than start again.
@quan can this be closed as a duplicate?
Expired pages are still appearing in the search bar at the front end