When I click Add sharing invite in my ticket sharing settings, what is the third party system option and how can I use it?
This option allows you to use the Sharing Agreements API to connect a third-party system as a ticket sharing recipient.
This type of connection requires custom code which is not directly supported. You are responsible for the code that you implement to share tickets with a third party outside of your Zendesk account and making sure that the API calls do not exceed the rate limits.
For more information on ticket sharing, see the article: Sharing tickets with other Support accounts.