With fellows, it can get a bit trickier than with residents. While fellows are typically fully licensed physicians, if they are working for a GME approved fellowship, they are fall under the same exact guidelines as residents. In those situations, you follow the same billing guidelines as residents - attestations, etc.
However, sometimes fellows moonlight or are training in a NON GME approved fellowship. In those circumstances, they are a fully licensed physician and billable as such.
Here's my real life situation regarding fellows. At our gyn oncology practice, we sponsor a one year non-GME fellowship in complex pelvic surgery and minimally invasive procedures. It is designed for an ob/gyn who has already completed residency who wants to gain more surgical training than the typical ob/gyn program provides. Training is mostly by gyn oncology, but also touch into urogynecology. Most of our graduating fellows do not do much OB work, but rather become the expert surgeon for non OB cases in an ob/gyn practice. Since the fellow is in a NON GME program, their services are fully billable under their own credentials. If we started up a 3-4 year gyn oncology GME fellowship, those fellows would not be billable, unless working outside their fellowship.
Here is an old, but still relevant prior thread about it.
https://www.aapc.com/discuss/threads/fellow-vs-resident.10087/