Hawkeye's line about hope in Avengers: Endgame became one of Clint Barton's defining moments in the MCU, but Fringe had the idea first. From the minds of J. J. Abrams, Alex Kurtzman and Roberto Orci, Fringe first aired in 2008 and ran for five seasons, gaining a cult following with its cutting-edge science fiction and unmistakable character chemistry. Fringe's central trio of characters included skeptical FBI agent, Olivia, the archetypal mad scientist, Walter, and his brash, estranged child prodigy son, Peter. The relationship between these three figures drove Fringe forward and has maintained the show's popularity long after its conclusion.
After losing his entire family in the aftermath of Thanos' Infinity Gauntlet-fueled snap, Jeremy Renner's Hawkeye takes a dark turn. Adopting the persona of Ronin, the former Avenger becomes a brutal vigilante with very few qualms about using lethal force against criminals in all corners of the world. When Hawkeye's former workmates hatch their "Time Heist" plan, however, Black Widow seeks out her best friend to bring him back into the superhero fold.
When Natasha mentions that there might be a way to undo all of his pain, Hawkeye responds with the line "Don't. Don't give me hope." This quote would later take on a life of its own as an online meme, for example if someone suggested there was a way Spider-Man might be able to return to the MCU. Interestingly, there's a fair similarity between Hawkeye's line and a quote from Peter Bishop in Fringe's very first episode.
In the Fringe team's debut investigation, an unknown chemical is claiming the life of Olivia's love interest and the mentally unstable genius known as Walter Bishop is her only hope of saving him. When Walter suggests that he might be able to find a cure using some experimental scientific techniques, Peter chips in with, "Don't do that. Don't give her false hope." As first pointed out by Reddit user gianben123, this works as an amusing parallel to Hawkeye's famous line in Avengers: Endgame.
The only two differences between these quotes are Peter speaking about Olivia, rather than himself, and the addition of "false" but otherwise, it's largely the same. It's perhaps also worth noting that Peter may have had a vested interest in offing Olivia's current partner, since he eventually romances her himself. The similarity between these two scenes is most likely nothing more than an intriguing coincidence, of course, and with the word "hope" banded about endlessly in so many TV shows and movies, this kind of crossover was bound to happen eventually, and it wouldn't be too surprising if other similar variations of this same line existed somewhere out in the ether of film and television.
Still, perhaps if memes were as prevalent in 2008 as they are today, Fringe's Peter Bishop might've found himself all over social media instead of Avengers: Endgame's Clint Barton.
