Serverless-1.0.0-rc.1 enables to deploy an API to be accessible via a AWS API Gateway.
The question: I need the deployed API exposed via a custom domain with SSL certif
I think this topic deserves an update, so I will give it a try. Be sure to first create a certificate with Certificate Manager. Then be sure your "serverless user" has the right admin permissions to modify Route53 record sets. Then add the following to your serverless.yaml:
custom:
customDomain:
domainName: "api.example.com"
certificateName: "*.example.com"
createRoute53Record: true
plugins:
- serverless-domain-manager
Before you deploy run (this can take a while):
serverless create_domain
Source and additional options can be found here.