Yes, you can store date paste in the fridge. In fact, refrigeration helps prolong its shelf life by slowing down the growth of microorganisms and preserving its freshness. Make sure to store the date paste in an airtight container to prevent it from drying out or absorbing any odors from other foods in the fridge. When properly stored, date paste can last for several weeks to a few months in the refrigerator. Just be sure to check for any signs of spoilage, such as mold or off-putting odors, before consuming it.