1. A/B/O universe, Clint is the only omega on the team. The whole team gets trapped by a villain in a room pumped full of pheromones or something that is designed to make them lose control. Clint stays on one side, and the team on the other, and no one loses control before SHIELD gets to them, but the whole thing is broadcast to the public and afterwards there are questions about whether there should be an omega on the Avengers (This might have been the point?) (Also, might have been Clint/Coulson, but I'm not positive.)
2. Another A/B/O universe sort of. Villain of the week zaps Avengers into the bodies of alternate universe counterparts in an A/B/O universe and they're very awkward because they don't know how to control themselves. Clint is (again) the only Omega (do you get I like that trope) and is interested in the fact that makeup and backless shirts are considered fashion for omegas regardless of whether they're male or female. I think Nat was an alpha and had to deal with a penis-type organ, and I remember Tony being a beta. Steve was an alpha and screamed when he found out he had a knot? And when they got back to their own universe they found out other!Steve had had the same reaction when he found out he DIDN'T have a knot. I think OT6 and they go through at least one heat with Clint before figuring out how to change back.
3. Can't remember if it was a pairing or gen fic. Clint is part of a legitimate agency that nearly burns him out before he's recruited for SHIELD, and they send him constantly on wet works missions, and Clint gets less and less sure that they're doing good things, and at one point he almost shoots a kid under orders but instead packs up his gun and punches his handler in the face. SHIELD gets him eventually and they don't have him on a kill mission for a significant length of time, and when they finally do, they pick the worst scum possible and Coulson sits Clint down and carefully goes through every horrible thing the guy has done to make sure that Clint knows the kill is justified. Clint thinks he'll be fine but is actually really shaky and nauseous afterwards.