The post-midnight irregularities in equator and its adjcent regions, which have remained least explored so far, are investigated using the in situ electron density (Ne) measurements from 2019 to 2021 obtained by the China Seismo-Electromagnetic Satellite (CSES) in the topside ionosphere. The followings are salient points of our findings: 1) Equatorial and low latitude post-midnight irregularities are distributed along the dip equator, exhibiting a wavenumber 4 longitude variation pattern and a seasonal variation pattern characterized by peaks in summer and winter and valleys in spring and autumn during low solar activity (LSA) period in the topside ionosphere, 2) The longitude variation pattern of post-midnight irregularities aligns with that of the background Ne, with irregularities concentrated at the peaks of background Ne, 3) The occurrence rate of post-midnight irregularities increases significantly with higher solar flux, which can be attributed to the rapid increase in the background Ne under LSA conditions. Additionally, the growth rate of occurrence rate varies across different longitudes, with the Pacific and the Atlantic longitudes standing out as prominent regions, and 4) Post-midnight irregularities in the topside ionosphere may have two possible origins. One is irregularities generated at the lower altitudes that drift upward into the topside ionosphere, while the other is the irregularities generated directly in the topside ionosphere. The latter is supported by the presence of conditions conducive to irregularity generation in the topside ionosphere during midnight hours in LSA period. Given the scarcity of research on post-midnight irregularity compared to post-sunset irregularity, further investigations are essential to fully comprehend their generation mechanisms. The abundance of post-midnight Ne measurements from the CSES satellite offers a valuable opportunity for this research, which can enhance our understanding of post-midnight ionospheric dynamics, and their variations with solar activity.