I have added two custom fields to our Ticket layout. Company ID and Location ID.
The Fields page shows that in the API their names will be cf_company_id and cf_location_id.

When I submit a ticket through the API I get:
{"errorCode":"UNPROCESSABLE_ENTITY","message":"An extra parameter 'cf_company_id' is found"}

I have put the custom fields into their own block - neither the name "cf" or "customFields" for this black makes any difference