Well my Japanese isn't up to scratch to do anything but speculate, so speculation ahoy!
Her appearance and the fact she has clones of herself obviously bring the Ple series to mind. I believe Elpeo Ple was one of (or a clone of one of) Gihren Zabi's illegitimate offspring (as was Glemy Toto, also connected to the cloning program), so it's possible Alicia is another of Gihren's children (she seems a little young to be one of Degwin's) , or, that she is an attempt at a "second bite at the cherry" of the Ple series by scientists from Axis who fled to Mars, or, that the two programs were developed side by side.
Another possibility is that perhaps she is the original illegitimate child of Gihren who Elpeo Ple was cloned from. The theories of her being the child of Kycilia/Johnny Ridden or Gihren/Cecilia Irene are good ones, I think - perhaps the natural child secreted away to Mars after the fall of the Zabis, perhaps created in a laboratory with samples of genetic material (it strikes me as being in character for Gihren to have some sort of project like that in case he died). If you wanted to really go far out, you could say she is the artificially conceived child of Gihren and Kycilia using genetic material salvaged from their bodies after A Bao A Qu, as the Ple series cloning technique is stated to be able to select only the most beneficial genes during production. That way she'd certainly have the right to the Zabi surname, even if it is a bit icky.
But there's an important distinction between her and Elpeo or Ple 2 - Alicia Zabi, whether born naturally or artificially created in some cyber-newtype breeding program, is not cannon fodder, but rather in charge of ReZeon (and considered a Zabi, not just a relative). This makes me think that either she is indeed the child of a Zabi, or, if she were artificially created, it was in the aim of making a newtype uebermensch to lead the Zeon remnants on Mars, not some super soldier project.
Of course, there's still the chance she's a common or garden Ple clone who survived the battle of Axis and...somehow...made her way to Mars and ended up leading Zeon remnants there. But considering the mental conditioning those clones received, it seems very unlikely for one to become an authority figure. But to find out the real answer, I guess we'll just have to wait for a translation (or learn Japanese). Until then, let's have our imaginations run wild!