In a small saucepan, combine the water, sugar, and jalapeño slices. Bring to a gentle boil and stir until the sugar dissolves. Pour the hot syrup and jalapeño slices immediately over the peaches. Let cool to room temperature, then strain to remove the solids. Transfer to an airtight container and chill in the refrigerator until ready to use.
Place the peaches in a medium bowl and mash with a fork. Set aside.