Half of a 1/4 teaspoon would be 1/8 teaspoon. Knowing how to cut measurements down or increase measurements is a very important tool to understand, especially when making less of a recipe or cooking for a crowd, which often requires increasing the amounts of the ingredients used.
Other interesting measurements to know include 1/2 of a 1/4 teaspoon, which is a dash; 1/2 of 3/4 cup, which is 6 tablespoons; 1/3 of a 1/4 cup, which is 1 tablespoon plus 1 teaspoon; and 1/2 of a 1/3 cup, which is 2 tablespoons plus 2 teaspoons.
When making baked goods, it is usually a better idea to make the recipe with the full amount, and then freeze any unused items. If the item is something often made, such as pancake batter, the unused portion can be refrigerated to use within a day or two.