JDK Version

Which JDK version is certified to be compatible with Openfire v3.10.2 and v4.0.1 ?

Where is no such thing as “certified” here. But you can use JDK 1.8, which is most up to date and should work the best. Although it should also be possible to use JDK 1.7. That’s for development. If you mean for running Openfire (JRE then). It should also run on both 1.8 and 1.7.