Apple - Cannot install JDK 13.01 on Catalina

1. Open "System Preference".
2. Go to "Security & Privacy" then "General" tab
3. Click on the lock icon then enter the password.
4. There will be a button "Always Allow" to allow "jdk-13.0.1". Click on it.

Just run

xattr -d com.apple.quarantine jdk-13.0.1_osx-x64_bin.dmg

to remove the download quarantine flag attribute.

As per Utsav T's comment, it is important to unmount and remount the installer (jdk-13.0.1_osx-x64_bin.dmg) to make sure that the installer works correctly.

After removing the quarantine flag attribute, install as usual.

You can install it via Homebrew.

1. Install Homebrew.
2. Install Java with Homebrew by running

brew install --cask java

Note the installation path in the output, it should be something like

==> Moving Generic Artifact 'jdk-13.0.1.jdk' to '/Library/Java/JavaVirtualMachines/openjdk-13.0.1.jdk'.

3. Remove quarantine status from the just installed Java SDK by running

xattr -r -d com.apple.quarantine /Library/Java/JavaVirtualMachines/openjdk-13.0.1.jdk

(don't forget to replace the the path to JDK with the installation path from step 2, as the JDK version might change.)