Line two large baking sheets with parchment paper or Silpat baking mats. Fill a large bowl with ice water and set it aside.
Combine the sugar, corn syrup and 1/4 cup water in a small saucepan set over medium heat. Attach the candy thermometer to the interior of the saucepan.
Increase the heat to medium-high to bring the mix to a boil, stirring until the sugar has disolved. Using a small pastry brush dipped in water, wash down the sides of the saucepan to prevent crystals from forming.
Boil the mixture for 5 to 7 minutes until it reaches 310°F (hard-crack stage) on the candy thermometer. Immediately transfer the saucepan to the bowl of ice water, carefully submerging the sides but ensuring no water seeps into it. Swirl the pan for 10 to 15 seconds to help the mixture cool then remove the saucepan from the bowl of ice water. If you're using an extract, carefully swirl it into the mixture immediately after you remove the saucepan from the ice bath.
Working quickly, pour the syrup onto the baking sheets to form circles that are 2 to 3 inches in diameter. (Space the lollipops 3 to 4 inches apart to guarantee they don't run into each other.) Immediately press in the lollipop sticks and sprinkle the lollipops with your sprinkles or candy, lightly pressing the garnishes into the syrup. Let cool completely until fully hardened then carefully peel the lollipops off the baking sheet.