Your sapphire ring sounds beautiful! My favorite gemstones are blue sapphires. My darling husband who has now passed away gave me a sapphire engagement ring, he said it brought out the color of my eyes! The color of the sapphire in my engagement ring is the color of violets. It is also surrounded by diamonds like Princess Diana's engagement ring.
Could it be the mark for John Avery ( not James Avery)? The mark for John Avery are the two letters you describe: I A in a square. I believe John Avery was US Silversmith based in Connecticut. Are the initials in your ring in a square shape? They should be if it is John Avery.
You mentioned you bought the ring from an antique dealer so can we assume the ring is "antique" although it is marked 14K which is a common US gold standard but not sure when they started using the 14K mark in the USA?
By the way there is no dot between the two letters, I and A. Hope this might help in your search.