When an iPhone is stuck in restore mode, is there any chance of data recovery?

Sadly, your data is gone. Restore it, then update it. If by chance you synced data with iCloud, such as Photos, Notes, Messages, you can get those back by signing into the phone with the same Apple ID and turning those services back on.

rynlvr wrote:

No no, unfortunately not. So just to clarify, even though there is the option to update the iphone in itunes, that won’t bring back the data? I have tried updating but it’s not working. Thankyou for your support!

Updating or restoring the iPhone in iTunes will NOT restore the data if the phone is in restore mode. Backups MUST happen before something goes wrong.

Sorry, no, not from the phone. Did you make backups on your computer or iCloud?

The update option is more likely to update the iOS version running on the phone, which must be out of date.

Likely.

What is the exact message which was displayed on your iPhone Screen? Did it show a cable going to a computer?