I received a 100cc quad because previous owner couldn't get it to run. No ideas of brand or specifics.
I replaced all warn and damaged components, as well as the carb. This includes the battery, starter, ignition coil and relay. Fired right up and ran very well. Even under my weight (260lbs) it would easily do wheelies. Could hit 30mph on the road. My small son ran it with the limiter on for weeks without issue. Was more reliable than a new quad we bought.
about a month ago it started popping and backfiring at the limited WOT. I was able to smooth it out by adding a small amount of choke.
Recently, reliablity has dropped. Now it will run ok, still popping and sluggish.
I bought new jets for it as well as checked valve lash. Intake was about a full turn in.
wlWith no limiter and WOT, the RPMs are very unstable and it will buck enough to nearly throw me.
It idles well and even. Low to mid throttle is snappy and even. Mid to high gets a little sluggish.
I have increased the main jet to a 90, than to a 96 currently. The 96 is less stable than the 90.
My current reading indicates not enough fuel, but increasing size has made it less stable. As well as I only have one jet larger. Am I missing something? I have pulled and checked the carb each time I have adjusted the carb. Needle is 4th highest setting.

 

Clean carb out and put jet back to standard, check fuel flow from tank. Fit a new plug and try bike. If it still isn't running right, check exhaust for loose baffles etc. If that is OK, you mentioned having to turn inlet valve adjuster a full turn. Either previous owner got the lash badly wrong or something has worn in the valve mechanism, I would try a new coil and CDI first, but it could be a valve problem, which would require a top end strip and check of all components.