It's probably best to actually do one of these trivia nights first, and make sure it is very good and well attended and gets some local attention and publicity, at least all over unofficial X-Files tumblrs and all over websites that would be read by NYC geek types (just get anyone you know and anyone they know who is a fan to attend, and publicize it on here closer to when the actual event is gonna happen) before even thinking about trying to get some kind of "official" approval for what you're doing. even though The X-Files may not be quite at the level of fame right now of Nicki or Taylor or Weeknd or whatever, the people involved with the show are really busy right now actually finishing postproduction on the new episodes, Fox is busy trying to market it (and I know, you think you'll be helping them do that, but Fox have a very old school attitude and take a long time to understand how unpaid fans can help popularize their shows)... if you do the event (say, for season one) and it's too awesome and hip for Fox/the producers to ignore (and too big for them to try to shut down) then they will have to get behind it and you may even get some kind of statement of approval from Carter, or other writers, or DD (who is a New Yorker originally) or GA. But you should not really expect that- it's kind of unlikely- fans are ALWAYS doing things and although a trivia night could turn out to be amazing (and I'm sure you have a vision of how amazing it can be and you are working to make that happen- rather than like, ending up with three depressed fiftysomething dudes hanging out alone in a big room going "yeah man, Duane Barry, that was a wicked episode" and munching on a kale chip) it could also turn out not-amazing (as in the above description) and just the IDEA of a trivia night (unless there is some other part that goes with it that you haven't told us about- like a masked orgy or something) is nothing special enough in itself, as an IDEA, to get Carter/Fox/DD/GA's attention. And I'm not saying you should overcomplicate your idea. A trivia night that is amazingly fun and draws in a huge amount of people of all demographics (trending more toward twenties/thirties than fifties hopefully) in what is perceived as the hippest zip code in the country (maybe the world) yeah THAT will maybe interest them. but you have to DO that first, see, and then grow further from there. you can't expect them to hand you that popularity. and anyway- here's a secret of XF fandom you may already know- fans actually respect each other in many cases, more than we do Carter, Fox or anything "official." Carter and Fox are not hyper-litigious about trying to stop things that use the XF name. So long as it's clearly NOT making you any money, they won't even know about it until it happens and turns out really popular, and once it happens and gets popular (a best case scenario, right? it may happen and get little attention) they will not try to shut you down and at that point they will probably want to work WITH you. but right NOW before you've actually done it, contacting them may actually be a terrible idea, because if they even notice you and read your request (which they probably won't) their response right NOW (i.e. before you've DONE it, gotten grassroots fan support, and proven it's the real deal and not a money making scheme for yourself) may be to SHUT YOU DOWN legally, before you even get started. furthermore, there would be no benefit in terms of attracting more fans to the event if you DID get advance approval somehow so you can say it's official. fans COULDNT CARE LESS if an X-Files trivia night is "official" and Fox approved it, and might actually PREFER that it was unofficial because then it feels less corporate and less of an advertisement exploiting our fandom to sell something (i.e. not for you to sell something, but for Fox to sell the new show), and especially the hip kinds of fans you want to help publicize your event (i.e. not stupid IMDB addicts, but fashionable people in NYC) would actually not be as interested if it was "official"! then it might be less fun! people would have to follow the party line.

Here is my suggestion- do NOT contact Fox or anyone associated with the show. Work on making sure every XF fan in the area knows about it, and beyond the hardcore fans, also the people who havent watched the show before but may be thinking of doing so, like the hipster (apologies for using the term) in Brooklyn who may be interested but needs an excuse or some social reason (your event will be the excuse) to dive into it. Make sure there is physical publicity (fliers etc, really cool arty posters made by you or people you know) in the kinds of places the people in NYC you want to be there, will be hanging out anyway (cafes, clubs, any places where genre geeks would hang out, etc) and make sure there is lots and lots of awareness on the Internet, which you could do by contacting the most followed XF tumblrs (not official- just fan) and trying to get the word out.

Finally, when you ALREADY have all that critical mass behind you of people you expect to be attending, and the event is all planned and you're pretty sure it'll go great, ONLY at that point, try to hit up Kumail Nanjiani (a former Brooklynite himself) on Twitter or email, and briefly explain about your event and yourself and subtly ask if he's interested in mentioning it on Twitter or on his next podcast (if he does one before then). But save that step until you're already sure it'll go okay even without his extra support- don't come to him from a position of NEEDING him to support it, but like, he would be that one added thing that could push it way over the top from a popular local event that comes and goes, into a Thing. Also, be sure you invite (although obviously he will be too busy to accept- and no longer lives in NYC) Kumail and his wife Emily to attend the trivia contest.

So, once you've done all that, actually hold the first event (season one right) and hope and pray everything clicks and it works out... and IF it does... then hope people are all over social media (and maybe even some local media, i.e. Brooklyn Vegan and that kinda thing) "reporting" on it afterwards and generating interest to make the second season one even better. Now, once you reach THAT point, and there is an actual article you can point to in, say, Brooklyn Vegan that talks about how cool your trivia contest was and how popular it was among all the people of NYC... THEN you can think about contacting the official X-Files people and trying to get yourself certified as an official event. Although frankly, unless this secretly is a way you are hoping to make money by getting paid to do viral marketing and street-team stuff by Fox, I'm not really sure you'll benefit a whole lot by making it official anyway.