The current default lifetime for the verification link is 432,000 seconds (five days). You can change the URL lifetime in the Dashboard (Email > Templates > URL lifetime ).
As for customizing, if you want to take control of the access expired case what you can do is set the redirectTo url field to a url of a page in your application, this can be set in the dashboard. When the link is expired the user gets redirected to that url with error_description=Access expired appended to it, at which point you could check this value and handle it.
Please let me know if this solves your issue!
You mentioned this error occurred for a user that was already verified, can you please clarify if they were sent the email by mistake or if the email was old and they clicked on the link?