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 was 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 understood this to mean that he felt like he was being picked on. Kirk understood, having been similarly persecuted by Finnegan. (TOS: "Shore Leave")