Time machine external disk ejects before backup is complete I'm creating the first full backup on a new 3TB drive.  Time reports just over 1TB will be needed.  Drive returns a disconnect message and time machine stops after every 100-300mb.  

My Mac runs High Sierra OS - 10.13.5
This sounds like the connection to the drive is not stable.
Try using another cable and changing ports on your Mac and on your external Drive if it has multiple ports.

If the problem persists the device is probably faulty and needs to be replaced/repaired.