How can I add a filter to an export display?
is there any way to add the same filter for the REST Export display ?

On your regular View page, apply filter for something, and you'll see a URL query gets appended to your URL. For example, when I'm filtering by content type, for mine, I see:
mysite.com/page-view?title=&amp;type=article&amp;status=All&amp;langcode=All (This is based on the view filters I have).
Then all you have to do is append this query to your REST export URL.
mysite.com/rest-export?title=&amp;type=article&amp;status=All&amp;langcode=All (Assuming you have the same filters as your page view, they should've been added by default when you added the REST view).
You'll need to create documentation for this. So people that are using your API know what parameter names &amp; values are accepted.