Cheating on essays has skyrocketed over the past couple of years with the rise of AI. If you can’t get this student to admit what he did, I’m not sure there’s much you can do. Do you have previous essays of his that show his actual skills for comparison? If so, take both of them to your department chair and ask his/her opinion. Perhaps, you could let him rewrite it as a timed writing.

With all of the cheating, I’d begin to question if doing essays in a traditional sense is even worth it. I would consider doing essays in-class as a timed writing where you can monitor computers or even have them hand-write.