The comments by others as a response are correct in that elementary particles are dimensionless. One interesting point to add though is that only integer spin

The comments by others as a response are correct in that elementary particles are dimensionless. One interesting point to add though is that only integer spin particles (the force carrying bosons) can share quantum states, which means they can occupy the same point in space. Another way to say that is to say the opposite, i.e. that half-integer spin particles (the fermions, which includes quarks that make protons and neutrons as well as leptons like the electron) cannot occupy the same quantum state as each other, which is manifest by them obeying the pauli exclusion principle. So if you were to take two photons they can literally occupy the same point versus two electrons which cannot (with some exceptions noted below). They are both point particles and technically have no volume, but there is this extra rule about quantum states that prevent two electrons from sitting in precisely the same place if they share all other quantum characteristics. Since this rule applies only if those electrons share all other quantum states, that means that if two electrons have opposite spins, they can occupy the same point in space. The first valence shell in a atom is the lowest state that an electron can have in a stable orbit (think of it as a standing wave that exactly lines up in a circle). There is 'room' for only one electron when you view the electron as a wave, but that shell can hold 2 electrons because there can be one of each spin type. Anyway kind of long winded, but I think the exclusion principle is at the heart of what makes us intuitively think about the electron as having volume in space and a photon as not. All this stuff is really really cool, but you can tell why physicists have that itchy sensation that there is some deeper explanation that is underneath all these rules.