You can now manage ticket statuses through the Core API. Front released ticketing a couple months ago, which you can now access via the API if your company has the ticketing feature enabled.

The following is a summary of the new ticketing functionality available in the Core API:

• Conversation responses return status_id, status_category, and ticket_ids fields.
• Search for conversations in the open, waiting, or resolved ticketing statuses via the is operator.
• Use ticketing filters in the q query string parameter when listing conversations.
• Access new Statuses API routes: 
  • List company ticket statuses
  • Get ticket status
• Update the status_id of a conversation.
• Update conversation reminders with a waiting status_id.