How do I delete archived messages on my iPhone?

Hi 11mine,

Thanks for asking the Apple Support Communities about archived messages.

If you are asking about deleted text/sms/mms or iMessages, once deleted, you can delete them from the recently deleted, or restore them for 30 days then they are automatically deleted: Recover deleted text messages on your iPhone or iPad - Apple Support

If you mean emails, there are different options for different email accounts. Check these help articles:

Delete emails on your iPhone or iPad - Apple Support

Archive email in Mail on iCloud.com - Apple Support

Delete and recover emails in Mail on iPhone - Apple Support

If these articles do not help, please let us know what app you are in, and what messages exactly. Thanks.