Is it possible to have some subdomains on the public internet; some not?

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Yes, you can:

If you have a wildcard cert (requires building Caddy with a plugin for your DNS provider to solve the ACME DNS challenge), then you can use that pattern to set up your sites.

You can use the remote_ip matcher to reject requests that are coming from IP addresses that are non-private (and use abort to close the connections):

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