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There were actually many Estonians recruited to the supply forces of Swedish army during the Swedish era in Estonia. Also there were Estonian free men (the ones not bound by serfdom) who sometimes served as mercenaries. And since the Swedes used a lot of mercenaries in all of their wars, they were the easiest employers to find.
If your guess is true and your roots are somehow tied to Estonia, then I think the best bet would be The Great Northern War and the Swedish campaign through all Poland and to Ukraine that ended with the Battle of Poltava 1709.
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