Here is a recipe on ginger ale syrup (I saw it on youtube and tweaked it a bit :))
150 g of fresh ginger
150 g of brown sugar (add more if you want it sweeter)
30 g of honey (add more if you want it sweeter)
around 1/2 teaspoon of cinnamon (you can use 2 sticks instead)
50 ml of lemon juice
600 ml of water
1. Clean the ginger, peel it, and finely chop it in a food processor.
2. Put the chopped ginger, sugar, honey, cloves, cinnamon and water in a pot.
3. Cook it on low for about 25 min. It should only simmer not boil.
4. When it’s done cooking leave it to cool (you can also put the pot in ice cold water to make it cool faster).
5. When it’s cooled strain the liquid through a mesh strainer (squeeze as much liquid from the pulp as you can) and discard the ginger and cloves/cinnamon sticks (if you want you can leave a bit of the ginger pulp in the syrup).