401 redirection

Are you saying that you are getting a popup when you access the page and you don't want that? Have you seen this codeshare? It describes how to change the status code on a response. You could use the same concept to redirect the user instead of keeping the 401 status.

Right now when I access the page 1) I directly get a popup to enter user + password in header information the http status is appearing with HTTP/1.1 401 Unauthorized

2) if I do no provide credentials I then I get the "HTTP Error 401.2 - Unauthorized: Access is denied due to server configuration" webpage --> I would like to redirect it to an other website or even to an error page

thanls for the proposed codeshare but it is not helping in that case

is there any http response header that can differentiate 401.2 from 401? have you ever used http analyzer tool? it may be helpful to check the response header.

HttpFox

otherwise, you may have to identify 401.2 response from response body e.g. using stream profile/irule, HTTP::collect irule command.

How about this?

when HTTP_RESPONSE {
  if { [HTTP::status] == 401 }{
    HTTP::respond 302 Location "https://google.com"
  }
}