In American parlance, I am guessing that you are asking whether a carnival was set up on that location.
The next question (from us) is whether you are asking whether a carnival or fair was set up on the WTC site since the reconstruction began or whether anyone ever held a fair or carnival between the two towers while they were standing or whether the site was ever used as place to set up carnivals before the WTC was built.
Your question was OK. The fact that the landscape changed radically three times in 40 years just added some complexity to it.
I am not a New Yorker and have found nothing on the internet, but I would guess that the answer was “No.” It was pretty much a business-focused complex with no residential units that I recall. WTC 3 was a hotel and there was a shopping mall below street level, but the complex was not really amenable to pedestrian traffic. When first built, winds whipping off the towers actually made it occasionally dangerous to try to walk through the plaza. (I don’t recall what steps were taken to correct that.)
A genuine New Yorker might show up to correct my impressions, of course.