Hi @Yankee30 ,
You can have Windows Server 2003 domain-joined machines in an Active Directory Domain Services (ADDS) 2019 environment, as long as SMBv1 is enabled.
I do believe you would need to have SMBv1 enabled on your Domain Controllers, to enable SMBv1 you can have a look here:
How to detect, enable and disable SMBv1, SMBv2, and SMBv3 in Windows
https://learn.microsoft.com/en-us/windows-server/storage/file-server/troubleshoot/detect-enable-and-disable-smbv1-v2-v3
I understand your need of keeping the Windows Server 2003 machines, but I would just like to point out that it is very highly recommended to upgrade/get rid of them, as SMBv1 is also a high security risk.
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Best regards,
Leon