I bought this coin in the mid 1980s from a bid wall that the Worthy Coin Company ran in Boston. I know. Most of time when you see the words "bid wall" for a coin auction, you think of low priced, beat-up coins pinned to a bulletin board with tacks.
This wall had the bulletin board and the tacks, but many of the coins were anything but beat-up, low grade and cheap. I bought a lot of wonderful coins off that wall, and missed out of some that have since gone to fame and glory. My 1793 Chain Cent came off that wall along with my 1796 quarter. There was also what became the finest known 1804 dime that was sold there. I scraped together every dollar I had to try to buy it, but a dealer was there who was acting as an agent for someone else was bidding on it. He is a friend, and he nodded to me that he had reached his limit on a bid, but I was tapped out too. One of my faults has also been that I don't bid more money than I have.
At any rate the 1797, 13 stars
Half Dime is a very scarce coin. It shows up in the major auctions only about two or three times a year. Logan and McCloskey rated it as an R-6 (13 to 30 known). "Coin Facts" estimates that there are 40. I once thought that the number more like 50, but perhaps that number is too high. The coin is tough. This one said to be the "reject" when Valentine was picking the coins for his plates, but I don't know how true that is.
My grade on this piece when I bought was VF-25. NGC graded it VF-35.
Note the "7"s in the date. Both of them are too large. The indication to me is that this die was made all at once with no storage time before it was put into service. My theory was that it was made at the same time that the obverse die for the 1797, 16 star obverse die was put into service because both dies share the same large "7"s.