It is a random child according to Nicholas Meyer
Trek Historian John Tenuto states he spoke with Nicholas Meyer upon discovering an on-set photograph of the 'Khan baby'. Tenuto states that writer / director Meyer says that the infant was not Khan's, but shows that Khan's people are capable of reproducing
John: I got a whole slew of new ones [photographs], and I just
finished cleaning them and getting them ready and now I'm going to
start cataloging them. One of the things that is in here is the 'Khan
baby'.
Larry: Oh! Do you know why it was taken out?
John: Yeah, there had been a magazine many years ago that had published a photograph, a very grainy picture of a baby by the Genesis
torpedo. And the story in the magazine said that basically, [Larry
interupts], yeah, but it was a baby by the torpedo this was a baby by
the torpedo as it was detonating. So the idea was, this was Khan's
baby, that was sort of what the theme was, right? So, but you're right
Larry, there were babies there.
So, I have these photographs, and there are pictures of Nicholas
Meyer holding this kid, and he looks, he's got the Khan clothes on,
you know, it's not exactly Khan's outfit, but it's Khan's people's
clothes, you know? And it's a costume for sure. And then the second
cameraman is there, he's trying to film this kid crawling by the
torpedo as it's going to detonate, right? So, the original idea was
that they were going to basically show a baby, a toddler, by the
Genesis torpedo as it explodes. Which would have been horrifically
dark. But of course, it's the implication, right? If they have babies
on board, they're gonna die on the Reliant. That's the idea. So I
have all these, these pictures of them trying to film this moment. So
I asked Mr. Meyer about this. So, what happened was, the idea was to
show, it's not Khan's kid. It was just to show that Khan's people
were reproducing. And he just said the idea just, it didn't work. The
idea didn't work. The moment didn't work."
Source: http://trek.fm/the-ready-room/80 - 2 hours 22 minutes into the podcast