We compile a sample of X-ray-selected galaxy groups and clusters from the XMM-Newton serendipitous source catalogue (2XMMi-DR3) with optical confirmation and redshift measurement from the Sloan Digital Sky Survey (SDSS). The X-ray cluster candidates were selected from the 2XMMi-DR3 catalogue in the footprint of the SDSS-DR7. We developed a finding algorithm to search for overdensities of galaxies at the positions of the X-ray cluster candidates in the photometric redshift space and to measure the redshifts of the clusters from the SDSS data. The detection algorithm provides the photometric redshift of 530 galaxy clusters. Of these, 310 clusters have a spectroscopic redshift for at least one member galaxy. About 75 percent of the optically confirmed cluster sample are newly discovered X-ray clusters. Moreover, 301 systems are known as optically selected clusters in the literature while the remainder are new discoveries in X-ray and optical bands. The optically confirmed cluster sample spans a wide redshift range 0.03-0.70 (median z=0.32). In this paper, we present the catalogue of X-ray-selected galaxy groups and clusters from the 2XMMi/SDSS galaxy cluster survey. The catalogue has two subsamples: (i) a cluster sample comprising 345 objects with their X-ray spectroscopic temperature and flux from the spectral fitting, and (ii) a cluster sample consisting of 185 systems with their X-ray flux from the 2XMMi-DR3 catalogue, because their X-ray data are insufficient for spectral fitting. The updated L_X-T relation of the current sample with X-ray spectroscopic parameters is presented. We see no evidence for evolution in the slope and intrinsic scatter of the L_X-T relation with redshift when excluding the low-luminosity groups.