Fetch the field from Request Body when using x-amazon-apigateway-gateway-responses in API gateway

Question

Im trying to customize the error response in AWS API gateway using x-amazon-apigateway-gateway-responses . I see we can use $context to fetch error details. But How do I fetch the field Name/parameter name from the requestBody.

Here is my swagger code

`"/postStudent": {
      "put": {
        "operationId": "postStudent",
        "consumes": ["application/json"],
        "produces": ["application/json"],
        "parameters": [
          {
            "name": "x-request-id",
            "in": "header",
            "required": true,
            "type": "string"
          },
          {
          "name": "StudentRequest",
          "in": "body",
          "required": true,
          "schema": {
            "$ref": "#/definitions/StudentRequest"
          }
        }
        ],
        "responses": {
          "200": {
            "description": "200 response",
            "headers": {
              "x-request-id": {
                "type": "string"
              }
            }
          },
          "400": {
            "description": "400 response",
            "headers": {
              "x-request-id": {
                "type": "string"
              }
            }
          },
          "500": {
            "description": "500 response",
            "headers": {
              "x-request-id": {
                "type": "string"
              }
            }
          }
        },
        "security": [
          {
            "api_key": []
          }
        ],
        "x-amazon-apigateway-request-validator": "Validate body, query string parameters, and headers"
      }
    }
  },
"definitions": {
      "StudentRequest": {
          "title": "StudentRequest",
          "type": "object",
          "properties": {
            "studentRollNumber": {
              "type": "integer",
              "format": "int32"
            },
            "studentName": {
              "type": "string"

            },
            "section": {
              "type": "string"

            }
          },
          "required" : ["studentRollNumber"]


      }
        
    
  },
  "x-amazon-apigateway-gateway-responses": {
     "BAD_REQUEST_BODY": {
      "statusCode": 400,
      "responseTemplates": {
        "application/json": "{\r\n \"message\":\"Invalid field\", \r\n \"code\":\"677\"}"
      }
    },
}`

I want to fetch the field name **studentRollNumber **from the requestBody object if a invalid value is passed and return in the error response body as { message: Invalid Field studentRollNumber , code:677}

I tried using the following but none of them gives the requestBody parameters value '$context.error.responseType', '$context.error.message', '$context.error.validationErrorString', '$context.resourcePath', '$context.error.messageString', '$context.extendedRequestId' I referred to this documentation: https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-mapping-template-reference.html#context-variable-reference-access-logging-only