He is an overly ambitious character who began as a simple guard for the prison world Incarcecon who held a disdain for Kwarrel due to his reforming/calming, mentoring role he had for the other prisoners. He discovered Kwarrel's tunnel a few months before his use of it was realized and discovered blue crystals which had hallucinogenic, psychosis inducing effects on whomever inhales a dust variant, making the crystal the intergalactic equivalent of LSD, PCP, or similar drugs on Earth.
He seems to be pretty strict. He fears no one when the prisoners have their collars on. Only when the collars come off, he shows a lot of fear towards everyone. He most likely fears the Plumbers even more than the prisoners because if they find out about how Morgg is using the prisoners for his own gain, they will surely arrest him.
He has no powers. Since he was a guard he has a lot of guns and technology. Since he is now warden he can summon his robot guards whenever and instruct them to do what he wants. He also seems to be quite strong as he was able to hold his own against Kwarrel.
He uses this "Alien dream dust" to cause the prisoners to riot and take initiative on his ambitions. He caught Kwarrel using the riot as cover and escaping with Kevin and prevented their escape, but Kwarrel stayed behind brawling with Morgg while Kevin Levin managed to get away on Kwarrel's request. Morgg gains the upper hand long enough to use his blaster on him and it is this sacrifice that spurs Kevin's revenge when he is driven insane by absorbing the DNA from the Ultimatrix.
After the riot, sometime between the 6 years, Morgg managed to become the warden of Incarcecon, replacing all of the sentient guards with robots to keep the hallucinogenic crystals his own secret, and turning the prison into a labor camp, mining his hallucinogen and allowing Morgg to become an Intergalactic Drug Dealer. However, Kevin returns voluntarily as a prisoner and attempts to kill Morgg but his attempt is averted by Gwen Tennyson's magic because of what's going on at the prison and him trafficking drugs. Morgg is presumably handed over to the Plumbers to be tried for crimes of prison labor, drug trafficking and denying prison rights. The Null Void branch of Incarcecon will most likely be turned over to plumber jurisdiction and reforms will likely be made to the system in order to give a semblance of honor back to Incarcecon.
He is the main villain of the episode ...Nor Iron Bars a Cage, where he has prisoners working for him to dig out these blue crystal dust. He has robots who help him secure the place. In the end he is taken away by the Plumbers.