Originally Posted by
Adam-X
The answer is in X-Men #38.
After defeating Arcade (X-Force #29 & 30), Arcade tells Adam to go look for Carter Ryking. Carter Ryking (X-Men #38) tells Adam that his father worked with Milbury. But tells Adam to go look for Professor Xavier.
He never gets a chance to because in X-Men #41, he's seen fighting Eric the Red when Legion triggers AOA (and Adam and Eric are locked in crystalized combat).
We see Adam again, in Captain Marvel #2 and #3, and learn that after the time line was restored, Eric seized control of Adam's mind and sent him to kill Captain Marvel (Genis-Vell).
During the fight, Adam claps the Nega-Bands together on Genis, and it sunders the control Eric has over Adam.
So Adam and Genis team up - and confront Eric the Red, who explains Adam is the son of D'Ken and a human, and that he was made to be the heir of the Shi'ar Throne.
Adam uses his powers, and essentially causes a major explosion (supposedly/apparently) killing Eric the Red, and using the Nega bands to teleport and avoid the explosion.
Adam appears next in S.W.O.R.D. which confirms his half-breed Shi'ar heritage.
Then appears next in Dark Avengers (in very poor writing) - with others rebelling. He's defeated (along with the others).
Then next appears, during Fear Itself when Cyclops calls him in to help stop Juggernaut - he manages to cut Juggernaut, but Juggernaut just bleeds fire.
In regular continuity, that's his last appearance.
But he then appears in the Secret Wars Age of Apocalypse stuff - as Burner in all of the issues - and confirms that he is the (half?) brother of Cyclops and Alex (as their powers don't work on each other, similar to what we've seen with Alex and Scott).
He dies saving Alex and Scott, there.
He appears again (cameo) in X-Babies #4.
And then has a few appearances in X-Men '92, which is not considered normal continuity.