A persecution complex was a mindset or set of beliefs that lead one to feel persecuted or conspired against even if there was 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")
In 2268, as part of a ruse to fool the Romulans, Dr. McCoy mentioned "feelings of persecution" as being among the symptoms Kirk was apparently exhibiting. (TOS: "The Enterprise Incident")
In 2370, Quark claimed that, due to their constant suspicions of him, both Odo and Kira were responsible for the Ferengi developing a persecution complex. (DS9: "The Collaborator")