I have an issue of Sport Compact and it claims the Z tune skyline is the fastest production car in the quarter. Buy why is the Z tune considered a "Production car"? isn't that like calling a GT500 Super Snake a production car?

The numbers required to be considered a production car vary depending on the country, subject, etc.
FIA (FEDERATION INTERNATIONALE DE L'AUTOMOBILE) consider 50 to be a production vehicle which would not include the Z-Tune's 20. I belive that's the number required for the US also. I don't know what the number is required to be in Japan.
Regardless, the GT500 Super Snake is a bad comparison, only one was ever made by Shelby. 50 were intended to be made (which would have made it a production vehicle) but VIN# 67402F4A00544 was the only one.
Also, I wouldn't believe everything Sport Compact publishes. I've seen them publish some pretty inaccurate translations, statements, figures, etc.

Only 1 Super Snake? There should be alot more than just 1. Unique Performance in Farmers Branch TX makes and sells them. Thanks for filling me in though. Beautiful skyline by the way.

So does anyone have any proof like a video or something the backs up this claim?

I think there was a BestMotoring clip but I'm not sure.