I am just wondering if we can use the Release pipeline service to deploy the build on our clients' on-prem servers or the services are restricted to use within the organization?
Can we use release pipeline to deploy app on client's on-premises server?
Yes.
If you are using the classic UI release pipeline, firstly, you need to create a deployment group on your client's on-premises server and use it in your release pipeline.
Then you can use some tasks to deploy, such as IIS Web App Deploy task, Copy Files task.
If you are using the yaml pipeline, you need to create a self-hosted agent on client's on-premises server.
You can click Self-hosted Windows agents for creating Windows agents, Self-hosted Linux agents for Linux and Self-hosted macOS agents for macOS.
The following steps are similar to those in the classic UI pipeline.