Boil water and sugar in a saucepan over medium-high heat until sugar dissolves. Cool and stir in corn syrup.
Reserve 1/4 cup sugar syrup; set aside. Dissolve instant espresso granules in 1 1/4 cups sugar syrup while still warm; cool to room temperature. Combine half-and-half with reserved 1/4 cup syrup. Divide half-and-half mixture evenly among ice pop molds. Divide espresso mixture among molds. Cover and insert craft sticks; freeze 6 hours or until thoroughly frozen.