Enabling Private APIs with Custom Domain Names (AWS API Gateway)
Amazon API Gateway does not support Custom domain names for Private APIs (as of this post). But there’s a pretty easy work around that involves a few steps. Update: Heeki Park has made this an official AWS solution — check it out here!!
When you create a private API, you target a VPC Endpoint that places ENIs into the subnets you configure. This allows your private VPC resources to reach the private API endpoint.
However, unlike public APIs — you cannot create a Custom Domain name for your API ……