Amazon Web Services announced the integration of AWS Marketplace and API Gateway last month.
Now lets see how this can help AWS SaaS startups
AWS marketplace has over 3500 software listing and an active customer base of over 100k users. So now you have direct access to AWS customer base. A new channel to reach out to your customers. Secondly, the heavy lifting of managing billing is already taken care by AWS. This has brought down your efforts on marketing and maintenance.
You can get started with these simple steps. I assume you already have the API built on the API Gateway.
Identify the API you want to sell on AWS Marketplace
Package the API into usage plans ( For example in a silver plan you can offer 1000 API Calls, for the gold one 10,000 etc)