Add the water and allulose to a small saucepan. Heat over medium heat, stirring occasionally, until the allulose is completely dissolved. Bring the mixture to a gentle simmer and cook for about 3–5 minutes.
Remove the saucepan from the heat. Allow the syrup to cool for a few minutes, then stir in 1/2 teaspoon peppermint extract.
Taste carefully once it has cooled slightly. If you want a stronger peppermint flavor, add more extract a few drops at a time.
If you want a slightly thicker syrup, whisk in a very small amount of xanthan gum while the syrup is still warm. Start with just 1/8 teaspoon because too much can make the syrup slimy rather than syrupy.
Allow the syrup to cool completely. Pour into a jar or bottle and store in the refrigerator.
Use as desired. I also added it to cream cheese frosting for a peppermint frosting.