Can you pull records with the API and not duplicate prior exports?

Is it possible to hit up the API and pull only new responses since the last pull, and is there a way to only pull particular fields from the survey? The code I'm currently using is:

downloadRequestUrl = baseUrl
downloadRequestPayload = '{"format":"' + fileFormat + '","surveyId":"' + surveyId + '"}'
downloadRequestResponse = requests.request("POST", downloadRequestUrl, data=downloadRequestPayload, headers=headers)
progressId = downloadRequestResponse.json()["result"]["id"]
print(downloadRequestResponse.text)

Thanks