In a small glass measuring cup, stir together the yeast, 3 tablespoons warm water and 1 teaspoon sugar. Allow to sit for 10 minutes until it foams.
In a large bowl, whisk together the flour and sugar. In a medium bowl, mix together the yeast mixture, egg, melted margarine, water, rum extract ,zest and salt.
Make a well in the center of the dry ingredients and add the wet ingredients. Mix with a wooden spoon until all ingredients are incorporated and a dough forms. Turn out dough onto a well-floured work surface and knead for about 5 minutes until smooth and elastic. Add additional flour, a tablespoon at a time, if dough is too sticky. Form into a ball, dust with flour and place in a bowl. Cover and allow to rise in a warm place until doubled in size, 1 to 1 1/2 hours. Knead gently to remove bubbles.
Divide dough into two parts. On a lightly floured work surface, roll each part into a log about 16 inches long. Cut each log into 12 pieces. Roll each piece into a ball and flatten out into a 3 1/2 inch diameter round. Place 1 scant teaspoon of jam in the center of the dough. Turn up the sides of the dough to meet each other, pinch tightly and reshape the dough into a ball. Place balls on a floured tray.
Heat oil in a medium pot over medium-high heat to a temperature of 340. Place 3 donuts into the oil at a time and fry for about 2 minutes per side until nicely browned. Place on a tray lined with paper towels.
To serve, place on a serving dish and sprinkle with confectioners' sugar.