January Jones Still Won't Name Her Baby's Father

The baby daddy drama continues!

January Jones has kept the identity of her baby's daddy a secret since announcing her pregnancy in late April.

She gave birth September 13, and new court docs show that she still hasn't named her baby's daddy -- son Xander Dane Jones has no name listed under "father" on his birth certificate! The space is blank!

So what's with all the secrecy?

Speculation ran rampant when January first came forward with her pregnancy news that the baby daddy was X-Men: First Class director Matthew Vaughn ... and that January had to keep it a secret because Matthew, 40, is married to supermodel Claudia Schiffer, 41.

Jones and Vaughn supposedly became close while on the set of X-Men.

SNL funnyman Jason Sudeikis, who January dated earlier this year, was also rumored to be the pop, but he denied it.

So Xander ... who's your daddy?!?