At a place, the length of the oscillating simple pendulum is made $\frac{1}{4}$ times keeping amplitude same then the total energy will be

The total energy for a simple pendulum in harmonic motion is $E = \frac{1}{2} m \omega^2 A^2$ with angular frequency $\omega = \sqrt{\frac{g}{L}}$. Substituting gives $E = \frac{1}{2} m \frac{g}{L} A^2$.

For initial length $L_1$, the energy is $E_1 = \frac{1}{2} m \frac{g}{L_1} A^2$. When the length becomes $L_2 = \frac{1}{4} L_1$ with amplitude unchanged, the new energy becomes

$E_2 = \frac{1}{2} m \frac{g}{\frac{1}{4} L_1} A^2 = 4 \left(\frac{1}{2} m \frac{g}{L_1} A^2\right) = 4 E_1$

The total energy increases by a factor of 4.

Final answer: $\boxed{\text{B}}$