I bought my device 2 years ago and there was no genuine check in wallet application at that time. I have some bitcoin on this wallet and I am not sure is my device genuine or not ? is it possible that my wallet has been compromised?
Your ledger device could show this issue for several reasons, and maybe it could be a problem with your faulty USB cable, or if you haven't updated your device firmware in a long time.
You can try to open Ledger Live app and go to
Settings-Help and then click on
Repair Your Ledger device.
You can follow the
guide from ledger website to check if your device is genuine, and it depends how exactly you purchased your wallet directly from their website or from some third party reseller.
I wrote before about many
attack vectors for hardware wallets and supply chain attack is one of them.
There is also evil maid attack if someone modified or replaced your wallet with identical tampered clone that is not genuine, so do NOT enter you seed words if this device or any other website is asking you to do it again.
Do not expect a "fast" response time given that they are probably still dealing with the huge level of support tickets raised after the data leak last year... but they will be the people most likely to be able to assist with determining why your device is showing that message, and what you can do about it. 
