The monthly security release window for Drupal 8 and 7 core will take place on Wednesday, June 15.
This does not mean that a Drupal core security release will necessarily take place on that date for any of the Drupal 8 or 7 branches, only that you should watch for one (and be ready to update your Drupal sites in the event that the Drupal security team decides to make a release).
There will be no bug fix or feature release on this date. The next window for a Drupal core patch (bug fix) release for all branches is Wednesday, July 06. The next scheduled minor (feature) release for Drupal 8 will be on Wednesday, October 5.
Drupal 6 is end-of-life and will not receive further security releases.