Troy -Bilt Riding Mower- confused about whether i have correct carburator

I have a Troy-Bilt Riding Mower m/n13BC26JD011, DOM-02/2013 with a  11.5 hp,POWER BILT ENGINE (m/n 217807), (TYPE 0984 G5) and (Code-121219ZA. i made  a trade for it last summer and it started and ran as it should until i  completed my mowing. When i started to mow another day i checked the oil and there was the odor of gas. Removed sparkplug and cranked 1 time and it blowed gas out the port. gas was overflowing  thru the tube coming from the block into the carb.  Gas tank was empty.  I thought the problem was the float in the carb stuck and let leak into places it is not supposed too. I removed the carb and cleaned carb, new plug,fuel filter, gas lines,  and new gasoline. Reinstall the carb and it run as it was supposed but as soon as i turned the key switch to off fuel started .leaking from carb.. Ordered new aftermarket carb kit and nstalled it. Again starts,runs,stops running and fuel continues  to leak. Is my carb the wrong one to use with this model. I looked at parts designs and have seen 2 different types of carbs. The type of mine does not have the solenoid at the bottom of the carb.. Could my problem be that i need the carb with the solenoid? If anyone could get the correct part number of the 2 carbs used this model would be very helpful.
Kindest Regards
Jerry Howard

That Nikki carb, (2 screws holding the bowl on) is problematic.
 
Part #137, the gasket between the plastic white assembly and the aluminum body
tends to leak especially if not installed fully, correctly in the white part: 
 
https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/briggs-stratton-engine/200000-399999-series/217800-to-217899/217807-0984-g5/carburetor-kit-carburetor-overhaul 
 
The separate, little "o-ring" is the main culprit. 
 
It must be installed in the carb body first,
a lil bit of di-electric grease applied, then the white part carefully inserted.  Any nicks, "roll overs", etc and it WILL leak fuel thru the carb...