John A. Griffith/Griffiths was the brother of better known gunsmith Joseph Griffith of Louisville, Kentucky. John was born in England in 1803, worked at Harpers Ferry with his four brothers, and then went to Cincinnati, Ohio in 1834. He moved to Louisville and worked briefly with his brother Joseph in 1837, then returned to Cincinnati where he worked until his death in 1865. John added an "s" to the end of his last name and was known as John Griffiths for many years in Cincinnati. He may have added the "s" to identify his guns from his better known brother's work from Louisville, when most guns were commonly signed with a first initial and last name.
This fowler looks very similar to fowlers sold by Joseph Griffith in Louisville, who traveled to England periodically to purchase many pistols and fowlers which he imported, marked with his name on the barrel, and sold in his shop. This may well be in imported piece marked by John Griffiths for re-sale in his Cincinnati shop.