AWS Lambda and API Gateway can be a good choice for serverless options, as you’ll only be paying for what you use rather than a server instance which could be sitting idle at times and still cost you money.
I’m actually working right now on a tutorial on how to use Lambda and API gateway as an EBS, but as that’s still a work in progress I’ll refer you to my Webhooks tutorial https://github.com/thedist/Twitch-Webhook-AWS-Tutorial which should serve as a base to work from towards what you need as it focuses a lot on API Gateway and Lambda, you can just skip the DynamoDB parts and focus on the Lambda functions (which you’ll put in your own code for verifying the JWT token and doing whatever else you need to handle) and the API Gateway part of the tutorial will show you how to setup routes to your Lambda functions.
Twitch also offer an AWS Credits program https://dev.twitch.tv/extensions/aws/ which is one of the reasons why AWS is often recommended (Amazon owns Twitch, so no surprise it’s the go to recommendation by Twitch lol) as that can potentially cover the costs during development.
There are other services out there that also are pay for only what you use, but my experience is with AWS so I’ll let others weigh in with other suggestions.