1.25 mls. There is no standard conversion of 1/4 tsp to weight, since this varies depending on the density of what you are weighing.
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A teaspoon contains 1/6 of a fluid ounce. 1/4 teaspoon would be 1/24 ounce.
1/4 teaspoon would be 1.25 ml at the standard conversion (1 teaspoon = 5 ml, 1 ounce = approx 30 ml)