How to setup Lambda Authorizer for a REST API added in Amplify,

This is how I solved it. amplify override API to create an overrides.ts file and add the following.

 // Create a lambda authorizer
  resources.restApi.addPropertyOverride("Body.securityDefinitions", {
    Custom: {
      type: "apiKey",
      name: "Authorization",
      in: "header",
      "x-amazon-apigateway-authtype": "custom",
      "x-amazon-apigateway-authorizer": {
        type: "request",
        authorizerUri: {
          "Fn::Sub":
            "arn:aws:apigateway:${AWS::Region}:lambda:path/2015-03-31/functions/arn:aws:lambda:${AWS::Region}:${AWS::AccountId}:function:${AuthorizerFunctionName}/invocations",
        },
        authorizerResultTtlInSeconds: 300,
        identitySource: "method.request.header.Authorization",
      },
    },
  });

  // For every path in your REST API, add the authorizer for all methods
  for (const path in resources.restApi.body.paths) {
    resources.restApi.addPropertyOverride(
      `Body.paths.${path}.x-amazon-apigateway-any-method.parameters`,
      [
        ...resources.restApi.body.paths[path]["x-amazon-apigateway-any-method"]
          .parameters,
        {
          name: "Authorization",
          in: "header",
          required: false,
          type: "string",
        },
      ]
    );
    // Use your new Cognito User Pool authorizer for security
    resources.restApi.addPropertyOverride(
      `Body.paths.${path}.x-amazon-apigateway-any-method.security`,
      [ { Custom: [], }, ]
    );
  }