Deleted Message conversation by accident.

If Messages in iCloud is enabled, the messages cannot be retrieved. If you're unsure if this feature is turned on, here's how to check: Use Messages in iCloud. If Messages in iCloud isn't turned on, and you have a backup that contains the messages, they can be restored with these steps: Restore your iPhone, iPad, or iPod touch from a backup. Keep in mind, any data that has been put onto your iPhone after the backup was created will be lost. If you have made a backup of the iPhone since you deleted the message, you will not be able to retrieve it either.

Unless you house your messages in iCloud, they are saved on your iPad backup. Restore that backup to retrieve the messages that were present when the backup was created.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support