How do I set my own local domain for automatic resolution?

When trying to resolve a PQDN (Partly Qualified Domain Name), the iOS DNS subsystem first tries to solve the hostname as provided and, in case of failure, concatenates it with the system domain prefix (normally assigned by your uplink gateway, for example: ".lan"). In order to specify a different domain to append, the server can push a special directive including the new name:

push "dhcp-option ADAPTER_DOMAIN_PREFIX foo.tld"

Note that this can work only when redirect-gateway or a VPN specific DNS has been configured. See the previous FAQ "How does iOS interpret pushed DNS servers and search domains?" to learn how to specify a DNS.