The following are the possible error messages related to an API call in Freshdesk:

400 Client or Validation Error The request body/query string is not in the correct format. For example, the Create a ticket API requires the requester_id field to be sent as part of the request and if it is missing, this status code is returned.
401 Authentication Failure Indicates that the Authorization header is either missing or incorrect. You can learn more about the Authorization header here.
403 Access Denied This indicates that the agent whose credentials were used in making this request was not authorized to perform this API call. It could be that this API call requires admin level credentials or perhaps the Freshdesk portal doesn't have the corresponding feature enabled. It could also indicate that the user has reached the maximum number of failed login attempts or that the account has reached the maximum number of agents
404 Requested Resource not Found This status code is returned when the request contains invalid ID/Freshdesk domain in the URL or an invalid URL itself. For example, an API call to retrieve a ticket with an invalid ID will return a HTTP 404 status code to let you know that no such ticket exists.
405 Method not allowed This API request used the wrong HTTP verb/method. For example, an API PUT request on /api/v2/tickets endpoint will return a HTTP 405 as /api/v2/tickets allows only GET and POST requests.
406 Unsupported Accept Header Only application/json and */* are supported.
When uploading files multipart/form-data is supported.
409 Inconsistent/Conflicting State The resource that is being created/updated is in an inconsistent or conflicting state. For example, if you attempt to Create a Contact with an email that is already associated with an existing user, this code will be returned.
415 Unsupported Content-type Content type application/xml is not supported. Only application/json is supported.
429 Rate Limit Exceeded The API rate limit allotted for your Freshdesk domain has been exhausted.
500 Unexpected Server Error Phew!! You can't do anything more here. This indicates an error at Freshdesk's side. Please email us your API script along with the response headers. We will reach you out to you and fix this ASAP.