2001 ZX6R idea issue

I have a 2001 ZX6R carb issue hope I can get some help with
The bike runs great other than when it gets Below 2000 RPM it slowly ideals down n dies it restarts but you gotta give a bit of throttle.
As well when you back off the gas she will do a small back fire.
I've cleaned the carbs but maybe something is a miss
New plugs and air filter even ran sea foam through her
Any ideas please shoot me a line
Thanks