Java for OS X 2015-001 is what you need. Of course, the download page still refers only to 10.7-10.11.
I know this has been addressed many times, but there seems to be a new wrinkle. When I go to the download page for the legacy runtime file, there is no button or other means of downloading. Photoshop/Illustrator etc. can't be used until I sort this. Does anyone know of a working download link please? I'm on El Capitan on a steam-driven 2008 Mac Pro, and this problem kicked in after I installed the latest security update today. That led to requiring recovery from a kernel panic episode and subsequent reinstallation of OSX.