Establish an interface VPC endpoint for API Gateway, attach an endpoint policy permitting all apigateway:* actions, disable private DNS naming for the VPC endpoint, configure an API resource policy to grant access from the VPC, and utilize the VPC endpoint's DNS name to access the API.

Set up an interface VPC endpoint for API Gateway, attach an endpoint policy allowing the execute-api:Invoke action, enable private DNS naming for the VPC endpoint, configure an API resource policy to allow access from the VPC endpoint, and use the API endpoint’s DNS names to access the API.

Deploy a Network Load Balancer (NLB) and create a VPC link, configure private integration between API Gateway and the NLB, and use the API endpoint’s DNS names to access the API.

Create an Application Load Balancer (ALB) and a VPC Link, configure private integration between API Gateway and the ALB, and use the ALB endpoint’s DNS name to access the API.