Azure DevOp deploy websites under one master website
We could not deploy one websites under another website, just could deploy web app under another web app.

We could only add the app under the website instead of the website. And based on the content of your question, it seems that your title is not accurate enough.
I would like to deploy 9 api's under one master Api, How do i do the
same.
If you want to deploy other 9 api's under one master Api, you could deploy those 9 api's under the same website on the IIS web app manage task:

And set the Virtual Application under the master Api App in the IIS Web App Deploy taskļ¼

The test result:
