Cleaned carburetor now the atv backfires, engine does not run at normal power, gas leaking from the overflow hose
Any suggestions?

 

Apparently you did not clean/rebuild the carb correctly. Revisit the carb, ensuring you install a new needle valve and seat, and ensuring float height is correctly.

 

This maybe one of the models with bad flywheel......2002 to 2006 has glued on magnets instead of machined magnets...If flywheel is out of time with engine it can cause alot of issues,,Like said about make sure carb is cleaned correct then may want to check for loose flywheel magnets,,If magnets are loose and have moved this could cause spark and fuel out of time which could cause backfire and overflow. and loss of power..also make sure has an new spark plug...Spark plug also in an timing part

 

Cleaning a carb is a NO NO, only a complete rebuild with a proper kit. Just taking a carb apart to clean it will normally cause more problems. Your float is stuck or needle valve is open or not adjusted properly. Timing may be an issue but need to address the carb first.

 

As you haven't posted that you figured it out, make sure the diaphram on the air slide piston is properly seated. Cleaning won't hurt a carb, only takes a spec of dirt the size of a pepper grain to mess up a jet. Probably the primary.Gas overflowing sound like the float is stuck or misadjusted.