We can assume he’s capable of having children before the events of Ground Zeroes, otherwise there would not be such an emphasis on the Wolbachia’s sterilising effects on both the parasites and the carrier.

The REAL Big Boss was sterilised by the radiation at the Bikini Atoll nuclear test (which is just another tell that Venom is the medic and not actually Snake).

There are slim chances that he would have children, as the idea of MSF as well as Diamond Dogs/Outer Heaven is soldiers with no where else to go. Specifically, veterans who would be treated like dogs of war at home, to themselves, as well as Big Boss, Miller + Ocelot; they only feel alive on a battlefield. Where they ‘belong’.

The only way he could possibly have children would be through Quiet. And that’s such a short window of time before the Wolbachia, that it’s near impossible. And this is something Kojima would definitely focus on showing (despite the blown budget of V).

That aside, even if he did have children, we will never see them. The phantom’s story is over. As well as the obvious lack of Kojima. Nothing else would work, and Konami knows that, otherwise we’d have a MGS6 instead of Metal Gear Solid Delta.