Hello,
If the old DirectAdmin is not missing a feature, then you could use a user level backup for creating a backup for a selected domain only. Then you could restore it on a new server.
If the old DirectAdmin is too old and missing the feature, then you will probably need to:
1. create a backup at admin level excluding Mails, Domains data
2. import backup to a new server
3. use rsync
to sync /home/admin/imap/jkl.com/
and /home/admin/domains/jkl.com/
to the new server.
4. remove asd.com, fgh.com from the new server (and related databases).