In-game, Martin is just a convenient plot device cleverly voiced by Sean Bean. It's never explained where he came from, other than the fact that he was Uriel VII's super-secret bastard (as opposed to his already existing and quite public bastard, Calaxes. Ugh, these people have no idea how to account for their own lore...but I digress).
Out-of-game, developer Ken Rolston wrote a piece in which Caius Cosades visits Uriel Septim's grave. In it, he mentions a woman named Gemile, who is basically said to be Martin's mother. Why he would hide THIS bastard from his wife, Caula Voria, and not the other one was not addressed. You can read the piece http://www.imperial-library.info/obscure_text/cosades_visit.shtml.
I don't think he was hiding Martin from his wife, he was hiding Martin from everyone (and not just those on the Mundus). Not to hide yet another bastard child, but to have an ace-in-the-hole because he knew full well what fate his and his other (possibly not even his) sons had in store. Dagon's hordes used the proverbial hammer on Kvatch because they had no idea where to stick the dagger like they did in the IC escape route.
Since in Caius's Visit to Uriel's Grave he mentions that he did the dirty with "Gemile" after the Warp in The West, it would indicate that he sired Martin after his captivity during the Simulacrum. It chronologically fits.