I would recommend first going to iCloud.com to see if your older emails are still on the server.
https://www.icloud.com/mail/
Sign in and use iCloud.com on an iPhone - Apple Support
If you see your older emails there, make sure that you have iCloud Mail turned on in your iCloud settings, Settings>Name>iCloud, and that you have enough device storage on your iPhone for all your emails to download, Settings>General>iPhone Storage.
If you are missing your older emails at iCloud.com, contact Apple Support. They usually can only restore iCloud emails if it's been 30 days or less since they went missing, but it's still worth a shot.
Contact - How to Contact Us - Apple
I also want to add that you might want to confirm that the emails you are looking for weren't coming from a third-party email, such as Gmail or Yahoo, etc. You can add those back to your Mail app.
Also, anything turned on in iCloud in your Settings is not backed up in an iCloud backup, but is backed up separately to iCloud, which also means that if you delete something (that is turned on in iCloud in Settings) it also gets deleted at iCloud.com and across devices that have that app turned on in iCloud.
What does iCloud back up? - Apple Support