There is no known ‘inside’ to an elementary point particle such as an electron. It is not a tiny sphere with an interior space, though back in 1920 physicists asked whether the space inside an electron was the same as outside. This was shortly before the wave/particle properties of matter were discovered by Louis deBroglie, which set the stage for quantum mechanics.
One way you might think of it is that it looks something like a globular star cluster like the one shown here called Messier 2, taken by the Hubble Space Telescope. (Credits: NASA, ESA, STScI, and A. Sarajedini (University of Florida)
The ’empty space’ within and near particles such as electrons and quarks is far more active and complex close to the electron than in the lower-energy ’empty space’ within the vastly-larger boundaries of atoms. There is no such thing as ’empty space’ anywhere in nature. There are only apparent ‘voids’ that SEEM not to contain matter or energy, but at the level of the quantum world, even ’empty’ voids are teeming with activity as particles come and go; created out of quantum fluctuations in any of a variety of fields in nature.
Heisenberg’s Uncertainty Principle all but guarantees the existence of such a dynamic, physical vacuum. Physicists, moreover, have conducted many experiments where the effects of these ghostly, half-real particles can be seen clearly. The level of activity that fills the physical vacuum is set by the energy at which the vacuum is ‘observed’. Within an atom, much of the activity is carried by ‘virtual photons’ that mediate the electromagnetic force, and by the occasional electron-positron pairs that appear and vanish. At very high energies, and correspondingly small length scales, the vacuum fills up with the comings and goings of even more high energy particles; quarks-antiquarks, gluons-antigluons, muons-antimuons, and a whole host of other particles and their anti-matter twins. Within the nucleus of an atom, gluons and their anti- particles are everywhere, going about their business to keep the quarks bound into the nuclear ‘quark-gluon plasma’, portions of which we see as protons and neutrons.
For electrons, enormous energy is stored in its electric field at small scales, so this allows more and more massive particle-antiparticle pairs to be created out of quantum fluctuations in this field.
So the ‘inside’ of an electron is an onion-like region of space where low energy virtual particles form the extended halo surrounding a core where more and more massive particle clouds are encountered.