My less than 1 month old iPhone 5s says that my accessory may not be certified by Apple even when it's not connected to anything, why?

I just got this iPhone 5s last month or so brand new out the box. I have only used the earphones and the charger that came in the box.

And after I went to sleep last night I left the phone off the charge and it says now when it's not even charging that the accessory I'm using isn't supported.

I let the phone die and then charged it back to 100 and it continues to say it...

I don't get why it's doing this because it's brand new and I use the cables that came in the box. I have AppleCare+ so if a replacement is needed will it cover this? I assume it's some form of software or hardware fault...

Any help is appreciated, thanks

I'll go to the apple store tomorrow and have a genius look at it just to be sure.