I couldn't work out ow to email you from this message board but...
a. there are many distinct jamieson/jameson families in the U.K., with roots in England, Scotland, and Northern Ireland. Then there's Ireland as well.
b. My family (I live in Manchester, England) name originated in Shetland, Scotland, and our ancestors are quite well documented back to about 1680. Most of our lot emigrated to the Scottish mainland, England, Australia or New Zealand when they left Shetland.
c. There are other completely distinct Jamieson families on Shetland. It is a very common name there. But I think they are probably all quite well documented. So if you have links with them you are probably in luck!
If you have any more information on possible starting points please post it. Which country are you in?
You are welcome to email me at firstname.lastname@example.org