A persecution complex was a mindset or set of beliefs that lead one to feel persecuted or conspired against even if there is no real threat. It is often associated with paranoia.
In 2267, James T. Kirk asked Leonard McCoy if he was getting a persecution complex after nobody seemed to believe his claim to have seen Alice and the White Rabbit. McCoy agreed, adding that he understood Kirk to mean that he felt like he was being picked on. Kirk sympathized, having been similarly persecuted by Finnegan as a Starfleet Academy cadet. (TOS: "Shore Leave")