Although we still don't know whether or not he'll make an appearance outside of Mulder and Scully's daydreams, it's already clear that William is important to The X-Files revival. Based on the first two episodes, it seems safe to assume that a large part of the reason both these characters are in such dark places is because they're haunted by the loss of their son. Although Scully gave William up for adoption in an effort to protect him, the children she encountered in the episode "Founder's Mutation" triggered her fear that he's out there somewhere suffering and fighting for his life. The William plotline is confusing to even to the most dedicated fans, mainly because his origins are so mysterious and we've been given precious few answers. But, since he's important to the revival's overall plot, it's worth exploring some theories about William on The X-Files.
As a quick refresher, Scully was left infertile after her abduction and her subsequent battle with cancer. She and Mulder unsuccessfully attempted to conceive a child through in vitro fertilization, and when she eventually did become pregnant it was considered a "miracle." During Season 9, William exhibited supernatural abilities and Scully feared for his life as he was stalked by the government. She made the decision to give him up for adoption on her own, because Mulder was in hiding and she's second-guessed the decision ever since. Although both Mulder and Scully believe her pregnancy was triggered by the abduction (because, you know, he turned out to be part alien), they consistently refer to William as "our son." This has caused some confusion among viewers — but it's most likely because they wanted a child together and planned to raise William as a couple, so (in that sense) it doesn't really matter whether or not Mulder is the biological father.
But, from a theoretical standpoint, it's possible that William doesn't have a biological father and he was "an experiment," as Scully says in "Founder's Mutation." Here are three possibilities about how William's story could be resolved:
1. He's Safe Because His Alien DNA Has Been Deactivated
In "Founder's Mutation," Scully expresses terror that, due to his alien DNA, William may be in grave danger. But, after closely re-watching the Season 9 episode "William," Reddit user susliks points out the likely possibility that the child's alien DNA was completely deactivated by Agent Spender. In that episode, Spender injects William with a magnetite substance in order to "cure" his telekinetic and supernatural powers. Although the alien genes could never be removed entirely, they could be "silenced," which would mean the government and/or super-soldiers could no longer track William.
However, Spender also says they'll never leave him alone — which probably means the government would continue to stalk William and attempt to reactivate his alien DNA at all costs. This would explain why Scully says, "they'll never forget what he was," when she gives William up for adoption and sends him to the middle of nowhere. Many people have questioned why Scully didn't simply go into hiding with her child, but the answer to that is fairly straightforward — she will always be traceable due to the chip in her neck and therefore William is safer when they're not together.
2. His Alien Powers Were Solely Inherited From Scully
During the show's initial run, it was speculated that Scully's pregnancy was triggered by the implant in her neck. This is still a definite possibility, but the revival has provided us with some new information about Scully. In "My Struggle," she tells Mulder that she mapped her entire genome and it's heavily implied that she has alien DNA. With this in mind, William's conception could have been a natural result of his parents' relationship — but Scully unwittingly passed on alien DNA to William. The above magnetite theory could still apply, but this potentially explains how and why William is Mulder's biological child and possesses alien DNA.
3. Mulder & Scully's Recent William Fantasies Actually Happened
This theory seems somewhat far-fetched, but it's worth exploring because anything is possible on The X-Files — Reddit user VladthePimpaler suggests that Mulder and Scully's recent fantasies about William weren't fantasies at all. In "My Struggle," they talk with Sveta about how abductees' true memories can be erased and then replaced with false ones — but sometimes the real memories come back in snippets. In this scenario, the adoption would be a planted memory and they actually did raise William for a period of time.
On the same thread, brandoss77 points out that some people can tell which memories are fake and others can't — so Mulder's "fantasy" depicts what actually happened to William and he's concealing this information from Scully because she's already experiencing so much grief. In this scenario, Mulder can differentiate between implanted memories, but Scully can't — so he lets her believe that William was adopted and could be safe, when in reality the child was abducted. If this is the case, showrunners are going to have a lot of explaining to do because viewers witnessed William's adoption in Season 9 — but it's definitely an interesting theory.
Right now, the million dollar question is whether or not William will make an appearance this season and clear things up himself. I may be reading too much into this, but perhaps Annabeth Gish's return for the revival is a clue. According to IMDb, Agent Reyes will only appear in the final episode, "My Struggle II," which is probably the episode that will provide the most information about William. Since Reyes and Scully are seemingly the only people who know William's whereabouts, perhaps she returns to help Mulder and Scully track down their son and get some answers.