An electron that is transitioning between two atomic states does not skip any intervening space. The idea of a quantum leap is highly misleading and commonly misunderstood. First of all, an electron is a quantum object. As such, it acts both as a wave and as a particle at the same time. When bound as part of an atom, an electron mostly acts like a wave. An atomic electron spreads out into cloud-like wave shapes called "orbitals". If you look closely at the various orbitals of an atom (for instance, the hydrogen atom), you see that they all overlap in space. Therefore, when an electron transitions from one atomic energy level to another energy level, it does not really go anywhere. It just changes shape. The orbital shapes with more fluctuations (with more highs, lows, and bends to its shape) contain more energy. In other words, when an electron transitions to a lower atomic energy level, its wave shape changes to have less kinks in it. But the electron does not "leap" anywhere.

Shown here are important electron transitions in the hydrogen atom. When an electron transitions between atomic states, it does not instantaneously leap. Public Domain Image, source: Christopher S. Baird.The wave behavior of an electron in an atom is very similar to the behavior of classical waves on a guitar string. When you pluck a guitar string, you excite standing waves in the string, which are what make the sound. A certain string can only experience certain types of standing waves because the string is clamped down on both ends. The types of waves allowed on a particular string are called its "harmonics". The harmonics of a string depend on the string's length, tension, and mass density. A particular guitar string (of a particular length, tension, and mass) can therefore only play a certain type of sound, which is a combination of its harmonics.