The following is based on Fallout cut content and has not been confirmed by canon sources.
Find Children spy in the Followers is one of the unimplemented side quests from Fallout. It can be assumed that the Followers of the Apocalypse had been infiltrated by the Children of the Cathedral, and the purpose of this quest was to find and apprehend the traitor.
Unfortunately, the traitor was either removed from the final version of the game or never implemented, effectively rendering the quest impossible to complete. This will also give the Followers of the Apocalypse a bad ending, regardless of what the Vault Dweller might try to do. With Fallout: New Vegas, the good ending is considered canon.