API Gateway billing

There is no metrics for API Gateway to show which clients are sending how many requests. Do you have access logs configured for the API stage? If not, I recommend enabling that and log variables like $context.identity.user, $context.identity.userAgent (if user-agent header can be used to determine a service). Once the access logs are generated, you can use CloudWatch Logs Insights to run a query to count the number of requests per user or any other attributes in logs.

• Setting up CloudWatch logging for a REST API in API Gateway
• API Gateway mapping template and access logging variable reference
• Analyzing log data with CloudWatch Logs Insights