Can I get deleted messages back on my phone?

Go to Settings > Your Name, iCloud, etc.

Tap iCloud

Are Messages turned on (green)?

If yes, your deleted messages cannot be restored

If Messages are not turned on in iCloud and you have a backup you made from before you deleted the messages, you can restore your phone from that backup, but be advised in doing so, depending on when the backup was made, your phone will be restored to the date the backup was made, meaning things like messages sent or received after the backup date will be gone.

I don't think you fully understood what I suggested. If Messages are turned in iCloud as I suggested you check, your messages are NOT contained in any backup as they synced with iCloud and when you deleted them they were deleted permanently.

The ONLY way they would be contained in a backup is if messages are NOT turned on iCLoud. So, if they are, restoring from a backup would not restore messages, because they wouldn't be there to begin with. And if you didn't have messages turned on iCloud and you want to restore from a backup, it is not something that is selective. In other words, when restoring from a backup it's all or nothing. So any messages sent or received after the date the backup was made will be gone.

Let me know if I have not cleared this up for you.

No. Because they are NOT in your backup if you synced with iCloud. They are gone.