I replied in wrong section just now, but I remember reading in last time somewhere (maybe in here comment section too) that the children are alpha butler and his omega mate but relinquish to miyauchi to raise.
But here is also possibility I misremember. Lol I hope I misremember because that wouls suck big time for miya to raise other people kid. but he is nice heart. and the name of this manga is yes desiny. so he accept his destiny of never being number one in the life of the alpha (he said this because he was jealous of his master, who has a destined mate)
really?? wow omegaverse unbelievable world,sorry I'm a newcomer in this society i don't really understand 100%.
what I know alpha and omega have a fate pairs. omega have a heat monthly with apheromones, and can pregnant with alpha or beta.
didn't beta is a normal person? from every page on opening chapter1.
idk about fate pairs. this particular story is about fated pairs but not all omegaverse are like that.
But yes, if you go back to this page
http://www.mangago.zone/read-manga/kashikomarimashita_destiny/mi/f934afad5dcaafc116852fb7793fd141_chapter-1/6/
it tells you that all humans became capable of pregnancy. so whether alpha, beta or omega you can give birth, whether female or male as well.
the difference between the three classes is that alpha have a higher amount of semen so they can impregnate others more easily.
Beta, as you said, are the most common of the three so yes they are the "normal" ones. But they can still have kids: male or female.
Omegas on the other hand, are hard to impregnate, they have reoccurring heats and are the most rare of the 3 types.
I think the biggest thing to take away from the omegaverse is that once an omega is bitten by an alpha, he can no longer have sex with another person. Their body will physically reject the a person that is not the biter.
KUDOU AND MIYAUCHI HAVE KIDS ITS TWO BOYS I THINK AHHHHH LIFE IS GOOD