Ron Guth: The 1797 Gripped Edge Half Cent is an extremely rare variety, with just over a dozen known, most of which are in low grade. The dies used to strike the Gripped Edge are the same used on the 1797 Low Head (Cohen 3a) and 1797 Lettered Edge (Cohen 3b) Half Cents. Ron Manley thinks the Gripped Edge Half Cents were struck later than the Lettered Edge Half Cents, but later than the Low Heads. The "gripping" consists of what appear to be a series of irregular indentations on the egde of the coin. The purpose of the gripping is unknown, but it is similar to experimental "gripped" edges on 1797 Large Cents. According to Roger Cohen (1981), the first appearance of a 1797 Gripped Edge Half Cent was in the 1907 sale of the Matthew Stickney Collection. Today, this variety ranks as one of the rarest and most desirable of all Half Cent varieties.
Sources and/or recommended reading:
"The Half Cent Die State Book 1793-1857" by Ronald P. Manley, Ph.D.
"American Half Cents (Second Edition)" by Roger S. Cohen, Jr.