How to reset the P2096 code error on my 05 Wrangler?

That is a strange issue, and this is the only thing I can find.

https://www.hyundai-forums.com/threads/p2096-and-p2196-codes.670358/

https://www.google.com/search?q=Hyundai+Sonata+2.4+GDI+Codes+P2196+and+P2096

..

P2096 OBD II Trouble Code Post Catalyst Fuel Trim System Too Lean Bank 1... https://repairpal.com/obd-ii-code-p2096-post-catalyst-fuel-trim-system-too-lean https://www.obd-codes.com/p2096

P2096- Post Catalyst Fuel Trim Sys Too Lean Bank1... It could be the result of bad gas or if you used fuel with a higher content of Ethanol. It could also mean that the post cat. converter O2 sensor on the driver side is bad. I would try filling up with a good quality gas (minimal Ethanol content), disconnect the negative terminal on the battery for a minute or so to reset the MAL (malfunction indicator light) and see if that takes care of it. If the code reappears, you may have a bad sensor, maybe ECU ECM PCM, worst case.... If you happen to need any info or ECU ECM PCM for this current vehicle (as they have a HIGH failure rate) or ANY other type of Car, diesel trucks small and big, SUV DIESELs ANYTHING etc, please call 888-672-4816 or 954-279-2040 and tell them Tim From FIXYA.COM sent you for FREE PROGRAMMING on YOUR NEW ECU ECM PCM DIESEL OR GAS COMPUTER!! Best Regards, -Tim

Did you replace the O2 sensor after the catalytic converter? This code is set by the rear O2 sensor. It usually indicates early failure or restricted catalytic converter. May want to have an exhaust back pressure test performed.

REPLACE REAR O2 SENSOR AND A MUST TO HAVE YOUR EC/PCM UPDATED. IF YOU BOUGHT YOUR O2 SENSOR FROM ANY OTHER PLACE THEN A JEEP DEALERSHIP THIS IS WHAT HAPPENS, THATS HOW THEY GET YOU TO GO TO THEM FOR REPAIRS, SORRY, BUT THE SAD TRUTH. GOOD LUCK

Fuel system .

WHAT EXACTLY MEANS THE CODE P2096 AND HOW I SHOULD FIX IT CRYSLER 300 2010

P2096=Post Catalyst Fuel Trim System Too Lean Bank 1,
drivers side was too lean at one time and set code,You should hhave the code erased and see if it returns again,

Here is more information about P2096
P2096-DOWN STREAM FUEL TRIM LEAN BANK 1

WHEN MONITORED 
With the engine running in closed loop mode, the ambient/battery temperature above (-7°C) 20°F , altitude below 8500 ft and fuel level greater than 15%.

SET CONDITION 
If the PCM multiplies short term compensation by long term adaptive and a certain percentage is exceeded for two trips, a freeze frame is stored, the MIL illuminates and a trouble code is stored. Two Trip Fault. Three good trips to turn off the MIL.

Here are some possible casuses:
Exhaust leak
Engine mechanical problem
02 sensor
02 signal circut
02 return circut
Fuel contamination

Good luck and hope this helps. 

It sounds like you're A/F ratio is too lean. Get yourself a service manual that way you will have the complete DTC error code list. www.promanuals.net has them for about 20 bucks.