In Detective Comics #988, DC introduced Bridgit Pike, Gotham's version of Firefly, as canon within official Batman lore. Although comics-based TV shows often take inspiration directly from the pages of comics, it rarely happens the other way around, yet that's what happened with this particular Batman villain.
In DC Comics, Firefly began life in 1952 as Garfield Lynns, a down on his luck special effects artist. But the most known iteration of the character is Ted Carson, who picked up the mantle of the villain in 1959. Carson was a wealthy man who gambled away most of his wealth, so he turned to a life of crime to pay his bills. Carson is the version of the character that existed in The New 52, as well as Rebirth. On the Gotham TV series, though, Firefly is Bridgit Pike, a woman. Pike was once a good friend of Selena Kyle, but as Firefly she chose a life of villainy with the other rogues on the show.
Pike never appeared in DC Comics, at least not until the latest issue of Detective Comics, issue #988. In that issue, Bruce Wayne, aka Batman, still feeling distraught over his canceled nuptials, is investigating the murder of a man shot by two separate guns. That leads him to an apartment building where he encounters a female Firefly. Alfred informs Bruce that this version of Firefly is probably the protege of Carson, a woman by the name of Bridgit Pike. Carson does eventually turn up, suggesting that there are currently two versions of Firefly in the Batman comics universe.
Pike's version of Firefly has appeared throughout Gotham over the past few seasons. It's also likely that she will turn up in Gotham's fifth and final season. That season will see the adaptation of the Batman: Zero Year story, where Gotham lies in ruins and the various factions of villains begin to rule the city. At the end of season 4, the villains ravaged Gotham City, setting up for what should present an epic finale for the series. It's also likely that the young Bruce Wayne will finally don the full Batman persona by the end of the season.
It's interesting that a Batman comic would take its cue from a television show that often presents itself as something happening in an alternate timeline. However, as is always the case with comics, many alternate timelines have their similarities, and in this case, that similarity is Bridgit Pike.