Open the Messages app
Swipe left on the conversation you want to delete
Tap Delete
To delete multiple conversations, tap Edit
Select the conversations you want to remove
Tap Delete
To delete a specific message in a conversation, open the conversation
Touch and hold the message
Tap More
Select the message or messages you want to delete
Tap the trash icon
Tap Delete Message
To delete all messages in a conversation, open the conversation
Tap the contact or group name at the top
Tap Info
Tap Delete Conversation
To remove messages from iCloud, go to Settings
Tap your name
Tap iCloud
Tap Messages
Turn off Messages in iCloud
Delete the messages from all devices signed in to the same Apple ID
Empty the Recently Deleted folder if available in your Messages app
Check other devices and delete the same messages there
Turn off message syncing before deleting if you want them removed only from the iPhone
Restart the iPhone after deleting to refresh message storage