Epsilon Adepts are one of the main Epsilon infantry, using their psychic powers to control an enemy's mind or killing nearby infantry with a psychic blast.
The PsiCorps uses Epsilon Elites instead, which are stronger and amphibious due to levitating above ground with their powers, but are otherwise still the same.
The very core members of Yuri's Epsilon Army, the Adepts are individuals with above average psychic abilities, allowing them to bend the will of others to suit their goals. They pose a significant threat to almost all soldiers and human-operated vehicles, turning their victims against their compatriots with a mere thought.
Adepts are capable of defending themselves against infantry with a potent psychic blast which overwhelms the brains of unshielded soldiers caught within, resulting in death. Though powerful opponents, Adepts are not able to control the minds of animals and are completely defenseless against robotic units.
In the prequel mission Archetype, PsiCorps Troopers (then only identified as Enemy Infantry) appear among the Allied forces. They can't do anything to Boris and Morales, who are both immune to mind control. Allied troops don't fire on them during the first half of the mission. As the mission progresses, however, these Troopers will attempt to mind-control Allied forces, thereby causing a commotion that alerts the entire Allied base.
In Act One, Epsilon Adepts are known as PsiCorps Troopers. They are the very first Epsilon unit introduced to the player, in Peacekeeper. They appear in almost all Epsilon Act One missions, and are buildable by PsiCorps from the Soviet Barracks (requiring a Palace or Battle Lab) in Moonlight as well as by Russia and the Latin Confederation in the following missions:
The Conqueror is the last mission where Adepts are used by PsiCorps, where they're tasked with mind controlling all eight Russian Topol-M platforms. After this mission, PsiCorps switches to Epsilon Elites.