Engine sputters during turns

The engine sputters on my 98 wrangler during turns when there is a quarter tank of gas or less. What is happening here?

If its only on turns its likely a weak fuel pump/or faulty sender seeing the level you see effects it.

I had a 97 that did the same thing; don't know for sure what caused it; never did it while 'wheeling or any other time for that matter, just higher-G turns. It only did it on right hand exit ramps, and a bit lower than you are saying; it was a good wake up call for me to fill 'er up. :)