I have only used Swagger with API Gateway with the old v0.5 version of serverless framework as there was a plugin that supported this easily. However, when serverless matured into v1.0 and up, at that time, there were no good plugins for Swagger integration.
Here are links you can check:
Serverless Github Issue: Swagger Integration
I don't personally use the above though as my big serverless projects are now using GraphQL (where API documentation is part of the standard tooling :-) instead of REST.