To determine which of the given points lies in the fourth quadrant, we need to recall that in the Cartesian coordinate system, the fourth quadrant is where $x > 0$ and $y 0$. This means point $A$ is in the second quadrant, not the fourth quadrant.
- For point $B$ with coordinates $(3,-7)$, we observe that $x > 0$ and $y 0$ and $y > 0$. These conditions place point $C$ in the first quadrant, not the fourth quadrant.
- Lastly, for point $D$ with coordinates $(-3,-7)$, it's found that $x 0$ and $y < 0$.

Therefore, the correct answer is $\boxed{B}$.