Here's a thought
Worst Wolverine coming from an ABO universe but him being a mutant fucked with his secondary gender....
He's both Alpha AND Omega.
He grows a knot just like any Alpha, but he also produces slick like other Omegas. He doesn't have a Rut or Heat, but a confusing, frustrating mixture of both at the same time.
Alphas don't want him and Omegas are scared of him.
Sometimes, a curious Beta approaches him, but they're just chasing thrills and always leave as soon as they get what they want from him. He never got pregnant, and as far as he knows, he never got anyone pregnant. He thinks he just shoots blanks and has the wrong body to create life. His Alpha side feels like a horrible Mate who can't provide, and his Omega self feels abandoned constantly.
He eventually stops accepting any offers from Betas and stays completely alone, even thru his "cycles."
That is until Wade snatched him up, dragging him thru the multiverse and into his home.