Maybe your function times out? Check the function logs to find out if it failed or not. If all OK in the function, enable execution logs in API Gateway and check why it reports a failure.
In addition to Uri - review the following url which does have some good tips to resolving the issue
Internal Server Error from API Gateway when sending queries through gateway to Lambda function connected to RDS database
Lambda response compression to API Gateway and clientasked 8 months ago
I am having an issue in API Gateway that says " No integration defined for method" when I attempt to deployasked 6 months ago
Uploading greater than 6 MB file to S3 through API Gateway results in Request too long error, Is that expected ?asked 6 months ago
API Gateway Timeouts from Lambdaasked 4 years ago
Deploy Lambda Function and API Gateway RESTasked 7 months ago
How to retrieve DATETIME fields from RDS database on S3 site via API Gateway and Lambda functionasked 5 months ago
How to associate an api key to an API Gateway websockets APIasked 3 years ago
Best way to publicly host a website of HTML/JS files and connect them to a RDS database?
Bypass CORS policy on S3-hosted site connected to RDS database