You can search for posts using the keyword search or retrieve posts and mentions related to a specific user.
Retrieving a user's posts and mentions supports cursor-based pagination so the response will include before and after cursors if the response contains multiple pages of data. Unlike standard cursor-based pagination, however, the response will not include previous or next fields, so you will have to use the before and after cursors to construct previous and next query strings manually in order to page through the returned data set.
curl -s -X GET \ https://graph.threads.net/17841405822304914/mentions?fields=id,username&access_token=EAADd...
{ "data": [ { "id": "18038...", "username": "keldo..." }, { "id": "17930...", "username": "ashla..." }, { "id": "17931...", "username": "jaypo..." } ] }