Another option might be running the following commands:

In order to install java 11:

sudo amazon-linux-extras install java-openjdk11

For java 8 you can try:

sudo yum install java-1.8.0-openjdk

Finally, if you want to switch between java versions run:

sudo alternatives --config java

Corretto is a build of OpenJDK. OpenJDK is source code that can be compiled into binaries by anyone. So if you want to install OpenJDK in Amazon Linux 2023, Corretto is a good choice.

Actually, Corretto identifies itself as OpenJDK:

$ sudo dnf install java-21-amazon-corretto
...
$ java --version
openjdk 21.0.1 2023-10-17 LTS
OpenJDK Runtime Environment Corretto-21.0.1.12.1 (build 21.0.1+12-LTS)
OpenJDK 64-Bit Server VM Corretto-21.0.1.12.1 (build 21.0.1+12-LTS, mixed mode, sharing)

See also: https://docs.aws.amazon.com/linux/al2023/ug/java.html

Corretto is a build of the Open Java Development Kit (OpenJDK) with long-term support from Amazon.

Historically, AL 2023 has provided extra OpenJDK packages, but they have been removed with release 2022.0.20220810:

In this release, we have removed the remaining openjdk packages, as we have shifted Amazon Linux 2022 to use Amazon Corretto as the JVM in the distribution.

• https://docs.aws.amazon.com/linux/al2023/release-notes/relnotes-2022.0.20220810.html

(The comments on the questions already contain lots of helpful information. Adding this answer anyway as a summary with references for future visitors.)

OpenJDK Java 15 is not available for Linux AMI, and I don't imagine it will be.

According to https://aws.amazon.com/amazon-linux-ami/. AMI has entered the maintenance support phase of its end-of-life. That means:

"During this maintenance support period:

• The Amazon Linux AMI will only receive critical and important security updates for a reduced set of packages.
• It will no longer be guaranteed to support new EC2 platform capabilities, or new AWS features."

Doing new stuff (i.e. involving Java 15) on AMI is a bad idea.

The replacement for AMI is Amazon Linux 2. I can't find a browsable list of packages, so I can't tell you whether Java is available for it. (But I doubt it.)

When I search for AWS Java 15, I find a link to the Amazon Corretto: Corretto 15 User Guide. This has installation instructions for a number of OSes, and the relevant ones for AMI and Amazon Linux 2 are as follows:

To use Corretto RPM repositories with the yum package manager, import the Corretto public key and then add the repository to the system list. For most systems, you must run the following commands:

sudo rpm --import https://yum.corretto.aws/corretto.key  
sudo curl -L -o /etc/yum.repos.d/corretto.repo https://yum.corretto.aws/corretto.repo

After the repository is added, you can install Corretto 15 by running this command:

sudo yum install -y java-15-amazon-corretto-devel

It is worth noting that many other vendors provide Java (many version) for generic Linux. One would expect that they could be installed on an AWS AMI instance. You would just need to follow the relevant instructions.