Deleted conversation

You're talking about deleted Messages?

Go to Settings > [your name] > iCloud.. is the switch turned on for Messages?

If the switch is turned on, you cannot recover your deleted Messages.

If the switch is turned off, you may be able to recover your deleted Messages if you have an iPhone backup that contains them. In which case you'd need to restore your iPhone to that backup. In doing so, you could lose other data between now and when you made your backup.

Locate backups of your iPhone, iPad, and iPod touch - Apple Support

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

See the article here:

https://www.macworld.co.uk/how-to/retrieve-deleted-texts-iphone-3636380/

But basically if you don't have a recent backup, you are out of luck.