Combine ginger, water, and sugar in small saucepan over medium heat. Bring to a simmer and reduce heat to low. Allow syrup to simmer for 10 minutes, stirring occasionally. Remove from heat and cool.
Strain syrup through sieve into blender; discard ginger (you can eat it too if you want!). Add peaches to blender and blend until smooth.
Pour mixture into popsicle molds and freeze until solid.
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