Was there anyone tested with Kobayashi Maru in Star Trek: Next Generation?
Not on screen, but in the novel A Rock and a Hard Place there's one person, a maverick who will be a temporary replacement for Riker, that had an unusual solution. Also in the short story 'Til Death (part of the The Sky's the Limit anthology), Riker's attempted solution is given.
I'm not going to say more about what was done or how, since that would be spoilers, but you can also find a little more info on Memory Alpha in their article on the Kobayashi Maru scenario. The direct link to the section with non-canon references is here. (That article also states a "similar" test was used in the 24th century, so it seems by The Next Generation they were using a different test.