B

Step 1: In a regular hexagon, the distance from the center to a vertex is given by the formula:
$$ r = a \cdot \frac{\sqrt{3}}{2} $$
Therefore, the distance from the center of the hexagon to each vertex (where charge $q$ is placed) is $r = \frac{a}{\sqrt{3}}$.

Step 2: The potential energy (U) of a charge $q_0$ placed in an electric field created by multiple point charges can be calculated using the formula:
$$ U = k \sum \frac{q_0 q}{r} $$
where $k$ is Coulomb's constant, $q$ is the charge at the vertices, and $r$ is the distance from the center to the charges.

Step 3: For a regular hexagon, there are 6 charges located at each vertex. Thus, the potential energy becomes:
$$ U = k q_0 \left( \frac{q}{r_1} + \frac{q}{r_2} + \frac{q}{r_3} + \frac{q}{r_4} + \frac{q}{r_5} + \frac{q}{r_6} \right) $$
Since all distances $r_i$ are equal to $r$, we can simplify it to:
$$ U = 6k \frac{q_0 q}{r} $$
Step 4: Substituting $r = a$ (the distance from the center of the hexagon to a vertex):
$$ U = 6k \frac{q_0 q}{a} $$
Final Step: Therefore, the potential energy of the charge $q_0$ placed at the center of the regular hexagon is:
$$ U = \frac{6k q_0 q}{a} $$
Hence, the answer is option B.