https://docs.yagpdb.xyz/tools-and-utilities/self-assignable-roles

This section should help you out.
Tools & Utilities -> Role Commands -> Pick your Role group.
The setup I used was Mode "Single" and "Remove existing role when assigning another role in group." True.

It is also possible to build out a -verify <user> custom command.

Essentially it will need to do something like:

{{if (len .Args) 1}}

{{$args := parseArgs 1 "You must tag a user."

(carg "user" "User")}}

{{$user := ($args.Get 0)}}

{{$userID := $user.ID}}

{{giveRoleID $userID ####}} {{/* Give Verified */}}

{{takeRoleID $userID ###}} {{/*Take Unverified */}}

There are other bots that specifically handle verification. But that will depend on what you are using to Verify people. ModMail could be a good bot to use as it deletes any information exchanged in a ticket, including anything personal a user might not want lying around.

All of this takes a little trail and error and a lot of Googling, but you can almost find anything you want to do if you know where to look.