Firstly, do not add the sub-domain to the DreamHost system via Add New Domain/Sub-Domain. If you have already added it, remove it and wait for it to be totally removed from the system before following the instructions below.
In the panel go to Domains -> Manage Domains, click on the small [DNS] link next to your parent domain, now, in the Add a DNS record to yourdomain.com section, add a DNS record with the following fields;
Name: The sub-domain name you require.
Value: The public IP address of your Debian box.
Click the Add Record Now! button and after a while your sub-domain will be pointing at your home IP address.
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