Starts and idles fine runs half throttle when fuel is applied

Question edited for FULL 'make model (what it is)', from 'banshee'.
Question moved from Motorcycles to correct Category.

Check spark plugs.
Clean Carb.
Check timing.

More here, it is a known issue.

https://www.google.com/search?q=Yamaha+banshee+atv+backfires

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Sounds like a frailed throttle cable, or that it might be rusted or mucked up with something. Would undo it on carb and see if it has full throttle movement on the cable. If you have not done this yourself before best to have it done professionally or do some read up good luck hope this helps

Sounds like a fuel blockage or your fuel pump is worn to the point that it can no longer provide the correct pressure.

tank airiation fuel tap filter tankfilter clean? sludge removedl a canister automotive engine cleaner for the fuel are by cleaning carburetor( if there is a L+R re-adjusted) are the gaskets changed and correct placed especially between cilinder and carburetor. there can be especially a small channel in it that it was wrong replaced or is the compression good enough ?
Compression is the very most important thing there is to look at the exhaust site to the piston that must be smooth otherwise there was a problem by overheating piston if there are grooves there can be a wrong adjusting of the carburetor or by a quality problem of the used gas

Assuming your diagnosis is good, how about the fuel filter and/or fuel pump?

If you are lucky, you might just need new fuel filter and the fuel bowl cleaned out, and maybe new air filter. If not so lucky you need carburetor rebuilt. Backfire is usaully caused by engine running too lean ( too much air for the amount of fuel present). Fuel bowls get gunk in them and the fuel needles and fuel jets get varnished up. The accelerator pump gets worn out gaskets and/or bellows and doesn't give the right amount of fuel mist when you accelerate.

Full Choke is indicative of a motor starved for fuel

Its either needs the fuel system, including professional carb cleaning, or there is a ignition system problem.
Its probably the carb!!!!!

The condition is call vapor lock.
Is there any missing heat shield?

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Use a bottle of yellow HEET dry gas to remove any moisture problem in the fuel.

how old is the fuel you are running