Psychosis disorders share overlapping symptoms and are characterized by a wide-spread breakdown in functional brain integration. Although neuroimaging studies have identified numerous connectivity abnormalities in affective and non-affective psychoses, whether they have specific or unique connectivity abnormalities, especially within the early stage is still poorly understood. The early phase of psychosis is a critical period with fewer chronic confounds and when treatment intervention may be most effective. In this work, we examined whole-brain functional network connectivity (FNC) from both static and dynamic perspectives in patients with affective psychosis (PAP) or with non-affective psychosis (PnAP) and healthy controls (HCs). A fully automated independent component analysis (ICA) pipeline called “Neuromark” was applied to high-quality functional magnetic resonance imaging (fMRI) data with 113 early-phase psychosis patients (32 PAP and 81 PnAP) and 52 HCs. Relative to the HCs, both psychosis groups showed common abnormalities in static FNC (sFNC) between the thalamus and sensorimotor domain, and between subcortical regions and the cerebellum. PAP had specifically decreased sFNC between the superior temporal gyrus and the paracentral lobule, and between the cerebellum and the middle temporal gyrus/inferior parietal lobule. On the other hand, PnAP showed increased sFNC between the fusiform gyrus and the superior medial frontal gyrus. Dynamic FNC (dFNC) was investigated using a combination of a sliding window approach, clustering analysis, and graph analysis. Three reoccurring brain states were identified, among which both psychosis groups had fewer occurrences in one antagonism state (state 2) and showed decreased network efficiency within an intermediate state (state 1). Compared with HCs and PnAP, PAP also showed a significantly increased number of state transitions, indicating more unstable brain connections in affective psychosis. We further found that the identified connectivity features were associated with the overall positive and negative syndrome scale, an assessment instrument for general psychopathology and positive symptoms. Our findings support the view that subcortical-cortical information processing is disrupted within five years of the initial onset of psychosis and provide new evidence that abnormalities in both static and dynamic connectivity consist of shared and unique features for the early affective and non-affective psychoses.