Brain connectivity represents the functional organization of the brain, which is an important indicator for evaluating neuropsychiatric disorders and treatment effects. Schizophrenia is associated with impaired functional connectivity but characterizing the complex abnormality patterns has been challenging. In this work, we used resting-state functional magnetic resonance imaging (fMRI) data to measure functional connectivity between 55 schizophrenia patients and 63 healthy controls across 246 regions of interest (ROIs) and extracted the disease-related connectivity patterns using energy landscape (EL) analysis. EL analysis captures the complexity of brain function in schizophrenia by focusing on functional brain state stability and region-specific dynamics. Age, sex, and smoker demographics between patients and controls were not significantly different. However, significant patient and control differences were found for the brief psychiatric rating scale (BPRS), auditory perceptual trait and state (APTS), visual perceptual trait and state (VPTS), working memory score, and processing speed score. We found that the brains of individuals with schizophrenia have abnormal energy landscape patterns between the right and left rostral lingual gyrus, and between the left lateral and orbital area in 12/47 regions. The results demonstrate the potential of the proposed imaging analysis workflow to identify potential connectivity biomarkers by indexing specific clinical features in schizophrenia patients.