Monthly Magazine & Newspapers/e-papers- You can read any number of publications you want to. For CLAT read The monthly magzines & news papers like Hindu, HT, The Economic Times, Indian Express etc. 

Current Affairs - Focus on National news, Editorial, Business and Sports sections. You should be updated with all the current information of it.

Make notes - You will be going through news from more than one source (magazine, paper, websites), so naturally, it becomes difficult to go back to those exact sources for revision. So put everything in one place. You can arrange your notes month-wise.

Annual Compendiums - You can go with Panorama (Pratiyogita Darpan’s) or Manorama.

Good Luck!