How long can I keep shrub syrup in the refrigerator I just made shrub syrup, by cooking fruit in sugar water (~0.5-1 cup of water and ~0.5-1 cup of sugar), sieving it, and mixing vinegar into it (~3 tablespoons of 10% vinegar on 1 cup) and I'd like to know how long I can roughly keep it when storing it in the refrigerator after I filled it into clean (but used) screw cap bottles.

What I maybe should add is, that I don't intend to store the syrup for a very long duration without using it. I will open the bottles now and then to take some of it out.

I am aware of this canonical question, but since it is a mixture of various things and since I'm not that well-versed in the intricacies of food storage (or cooking in general actually), I wasn't too sure what to take from it and maybe there might be a more detailed question possible applying to this type of food.
While, in general, vinegar retards the growth of certain bacteria (botulism), some allow the growth of others that are harmful. You should sterilize the glass containers by first washing them in hot water and soap, and then boiling for about 10 minutes and scalding the caps in boiling water. Filled and tightly sealed, your shrub should last about 6 months in the refrigerator. Opened and used occasionally, they should last 6-8 weeks, not unlike similar condiments that are kept refrigerated. Keep in mind that, should you include fruit in your original batch, it will age and, eventually, become a fruit vinegar.