Here are the steps to install a specific OpenJDK version in a local directory.
First find the Java version that you need by going here: https://jdk.java.net/archive
This snippet will download version 17
cd $HOME
mkdir LOCAL_JAVA
cd LOCAL_JAVA
# version 17
curl -LO https://download.java.net/java/GA/jdk17/0d483333a00540d886896bac774ff48b/35/GPL/openjdk-17_macos-aarch64_bin.tar.gz
tar -xvzf openjdk-17_macos-aarch64_bin.tar.gz
# version 24
# curl -LO https://download.java.net/java/GA/jdk24.0.1/24a58e0e276943138bf3e963e6291ac2/9/GPL/openjdk-24.0.1_macos-aarch64_bin.tar.gz
# tar -xvzf openjdk-24.0.1_macos-aarch64_bin.tar.gz
# if using v24 the commands will need to be modified to account for the name change
# check that the java binary is in place:
ls jdk-17.jdk/Contents/Home/bin/java
# run jar file
~/LOCAL_JAVA/jdk-17.jdk/Contents/Home/bin/java -jar $JAR_FILE