Normality (N) is a measure of concentration equivalent to the gram equivalent weight per liter of solution. For acids, it's determined by the amount of H⁺ ions that one molecule of acid can furnish in its reaction. Phosphorous acid, $H_3PO_3$, is a diprotic acid, meaning each molecule can furnish two H⁺ ions for reactions, despite having three hydrogen atoms, because only two of the hydrogen atoms are bonded in such a way that they can be ionized and participate in a reaction as protons ($H^+$).

To calculate the normality of a solution, you use the formula:

$N = M \times n$

where:

• $N$ is the normality,
• $M$ is the molarity of the solution, and
• $n$ is the number of moles of replaceable ions furnished by one mole of solute (in this case, the $H^+$ ions from phosphorus acid).

Given that the molarity ($M$) of phosphorus acid is 0.3 M, and it can furnish 2 $H^+$ ions per molecule, we use $n = 2$:

$N = 0.3 \,M \times 2 = 0.6\,N$

Therefore, the normality of the 0.3 M phosphorus acid ($H_3PO_3$) solution is 0.6 N. So, the correct option is:

Option D: 0.6