Open Settings on your iPhone or iPad
Tap your name at the top
Tap iCloud
Tap Messages
Turn off Use on this iPhone
Open the Messages app
Delete the messages or conversations you want removed
Go to Recently Deleted in Messages if available
Delete the messages or conversations there
On a Mac, open Messages
Select the conversation or message
Press Delete
Empty the Recently Deleted folder if available
Repeat on all devices signed in to the same Apple ID
Check iCloud.com if Messages sync is enabled there
Delete any synced message backups or related content if needed
Turn Messages in iCloud back on if you want future syncing enabled