By default the API will return result items starting from the beginning, it’s possible to skip any number of result items using the skipCount query parameter. This is typically used for implementing paging or infinite scrolling in clients.
The http://localhost:8080/alfresco/api/-default-/public/alfresco/versions/1/nodes/-my-/children?skipCount=2 request shows how you can skip the first two result items.
This query parameter is supported across all collection endpoints.