BIKE SPITS AND SPUTTERS BRIEFLY AT LOW IDLE SPEEDS.

fuel pump diafram weak

carb out of adjustment

Check the fuel pump , filter, throttle position sensor.

Don't use ethanol if you can avoid it. Check the manual to see if the bike wants hi test.

Check the inside of your combustion chamber and the inside of the rocker cover/ oil level. It sounds as if you have a blown head gasket.

Engine stalling and rough run issue at low speeds

This problem is commonly caused by a dirty automatic idle speed control valve and throttle valve. Buy a can of throttle valve cleaner (do not use carburetor spray cleaner!) from NAPA or Carquest (made by CRC chemicals) and spray it into the air intake while the engine is running, use up about 1/2 the can, engine will try to stall hold the speed up, shut it down and let it soak for 30 minutes, restart and blow out the remaining fluid, shut it down and disconnect the negative battery cable for 5 Min's to reset the base idle control

It sounds like it is running too rich (too much fuel). First, make sure the air filter is clean and that there are no intake leaks between the carburetor and the engine. Also, try a new spark plug (they can go bad without warning). Then, with the engine at normal operating temperature and idling, adjust the idle mixture screw to attain the highest idle speed. After this, set the idle to the correct speed using the idle speed adjustment screw.
Test ride. If it still spits and sputters at half to full throttle, then you will need to get a smaller main jet - or go to a less restrictive air filter, such as one by K&N.
Finally, I am not sure what prompted you to put a carburetor kit in, but if the bike had been sitting for any lenght of time (more than 6 months) make sure the carb isn't plugged up.

Clean out clogged fuel injectors

A cause for that would be an oxygen sensor getting wet, the one on the inlet side of the catalytic converter.

your low speed jets are stopped up ,the carbs need cleaning, go to walmart a buy some SEAFOAM, poor it in your gas tank ,start it up on choke, and when it start ot clear up take it off of choke, or ride it until it clears up. after it starts running good get it synchronized