Alpharius Omegon were (or are) the Primarchs of the Alpha Legion, and the twentieth (and twenty-first) son(s) of the Emperor.
Official Canon Edit
Alpharius Omegon's homeworld is completely unknown. All that is known is that they were found by Horus, not the Emperor. They were given command of the Alpha Legion; because the existance of the twins was a secret, Alpharius acted as the public face, while Omegon acted as the spymaster, though the two would switch places often. In addition, their Space Marines looked quite similar to them, and could be used as body doubles.
The Alpha Legion worked primarily through subterfuge and information warfare. They had a massive network of spies working for them, and their legion rarely operated under their own colors.
Horus Heresy Edit
Before the Horus Heresy began, the twins were approached by an Alien collective known as the Cabal. The Cabal warned them of Horus' imminent betrayal, and were given two options: If the Loyalists won, the Imperium would gradually decay and be overtaken by Chaos. But if Horus won, he would be so consumed by guilt that he would destroy Chaos for good, though humanity would be sacrificed in the process. Later however, the twins were also approached by Eldrad, who told them that he did not agree with the Cabal's prediction. While the Alpha Legion did side with Horus, that doesn't mean that both brothers were in agreement, or that the legion didn't fracture with its loyalist component siding with one of the brothers. The seemingly contradictory actions of the Alpha Legion and the fact that different legionnaires did fight under one or the other of the primarchs supports this.
Supposedly, Alpharius was killed by Rogal Dorn during the Siege of Terra, but was also killed by Roboute Guilliman. Whether they killed each brother, or body doubles, or if the story themselves are deliberate misinformation, is unknown.
TTS Canon Edit
The Emperor referenced Alpharius Omegon as a singular person, so it is still unconfirmed if he knew that they were two people instead of one. He did however said that he had "huge anonymity issues."