Line two large baking sheets with parchment paper. Unfold pastry sheets; place one sheet of pastry on each prepared baking sheet.
For almond filling, in a medium bowl, combine almond paste, 1/4 cup granulated sugar, and egg white. Beat with an electric mixer on medium speed until nearly smooth. Divide in half.
For each braid, spread half of the almond filling in a 3-inch strip down the center of each pastry sheet, leaving 1/2 inch unfilled along each end. Spread half of the preserves over filling. On both long sides, use kitchen scissors or a sharp knife to make 3-inch cuts from edge toward filling, spacing the cuts 1 inch apart. Starting at one end, alternately fold opposite strips of pastry at an angle across the filling, overlapping ends of strips in middle. Press down gently to seal.
In a small bowl, combine egg yolk and the water; brush over braids. Sprinkle with almonds and coarse sugar. Cover lightly with plastic wrap and let stand for 20 minutes. Remove and discard plastic wrap.
Preheat oven to 375 degrees F. Bake, one braid at a time, in the preheated oven for 30 to 35 minutes or until top and bottom are golden brown. Cool on a wire rack for 15 minutes. Cut into slices; serve warm.