External drives · Setting up your drive
How do I stop Time Machine asking to use my new external drive for backups?
Short answer: Click Don't Use and macOS won't ask again for that drive. If you accepted by mistake, remove the drive in System Settings → General → Time Machine. Nothing happens to the drive unless you agree.
Click Don't Use in the prompt. macOS remembers that choice for that drive and won't ask again. If you clicked Use as Backup Disk by mistake, open System Settings → General → Time Machine, select the drive and remove it as a backup destination.
Time Machine erases or takes over a drive only after you agree, so the prompt itself changes nothing. If you'd like Time Machine and your own files on one drive, give Time Machine its own volume — see adding a volume and using a Time Machine drive as the fast drive.