There's an official English version of this on webnovel with slightly better English.
https://www.webnovel.com/comic/the-duke's-hidden-baby-bogo!_17242463905015801
If you want to read raws, read here to help support the author: https://www.kuaikanmanhua.com/web/topic/2811/








So the people in this world treated Omegas so terribly, Omegas went extinct. The alpha and his team, supposedly world class people, find a rare Omega; and their attitude is, let's force this omega to have a kid and who cares if he dies afterward. They don't deserve Omegas. All these shitty people deserve to die out.
Uh, no. There was a disease that made everyone sick but killed off all the omegas. Rain was basically created in a lab by people trying to bring them back. His foster mother ran away with him and kept him hidden while the rest of the facility burned down. He's the only one left and there is clearly something not right physically with the lab-created omegas, so these science people believe he will die anyway.