It is hard to tell much from two small photos. The cheek-rest is typical for the later half-stock rifles from the Jamestown School.
Most of the patchbox is not visible in the photo, but the finial is not typical and unlike anything I have seen on a rifle from that school.
I have seen or owned 40 Jamestown rifles that were full-stock, flintlock, and had a patchbox. 3/4 of those have a twisted star patchbox finial with a daisy engraved around the screw. I have seen or owned six Jamestown rifles with Eagle patchboxes. All six were made by William Lamb. I think he was influenced by the Vogler family of gunsmiths 20 miles west of him in Salem. Thaddeus Gardner also made some rifles with non-typical patchboxes.
I would not usually expect to find a half-stock Jamestown rifle with the round cheek-rest that also has a patchbox, but then I found a rifle made by Chordy Whiteheart of Caswell County, North Carolina that has both...so what do I know.
Michael