His original purpose was to be the father of lullaby.

How ever the creator (our log recorder) was killed and turned into one of the subjects before he could tell him.

Static (the boss) then told him his job was to catch lullaby and hurt him. (For escaping and leaving the team that hurts the subjects)

So circus Xeno gore out to cause pain-

And stumbles across his son-

And then has a flashback-