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 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 and go to Settings-Help and 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.