After updating to OS 10.13.1 I got messages to update JDK, I have gone to the website, downloaded then installed the update. I then have the website run a check to see if I have the latest update. The site says that I, indeed, have the latest. But every time I boot up the Mac I get the message to update. I seem to recall this issue with an earlier update a couple of years back and don't remember how to resolve it.
You may need to download legacy Java that apple doesn't automatically ship anymore. That said, if you think you know which application may be what's requiring this, it may be a good idea to get rid of it if you don't need it. If you do need it, this should be the right download: https://support.apple.com/kb/dl1572?locale=en_US