Analysis on Alpharius - Alpha Legion
I believe alpharius and omegron do not exist, in that there was never a twins primarch. I do believe "alpharius" is the code name, the faux name the 20th primarch took up when finding horus. However I do believe he fabricated the story of having a twin to shroud himself in mystery, protection. I believe he was a single primarch, not a twin, and he purposefuly down played his power to have others underestimate him. On top of this I do believe perhaps he had the power of illusions, in that he was never actually seen, what his brother primarchs saw was just what he wanted them to see, a marine of his acting as him.
Now you ask wouldn't magnus or the emperor see that marine is different in warp energy then a primarch? Well I believe alpharius psyker abilities had to do with perception, reality manipulation or illusions. Thus he would take choice marines and shroud them in a faux guise to appear as him in every way, including warp signature, thus explaining why he was seen as the shortest primarch (tall space marine size).
I also believe alpharius set up the story of him being killed so he could operate more safely. As well as had the story of having his twin alive to still retain power in the legion and furher shroud himself in confusion.