In the outer shell of the atom, we find electrons. A bit simplified, they can be said to revolve around a very small and compact nucleus. This "cloud" of electrons gives the atom a diameter, which is about a tenth of a millionth mm, or expressed in powers of tens, 10-10 m.
The electron itself, which is a lepton with charge -1, is according to the Standard Model supposed to have zero size - it is point like. The electrons are tied to the positively charged nucleus by the electromagnetic interaction mediated by photons.
The nucleus of the atom consists of protons and neutrons. These are built up of quarks, which are tied to each other by the strong interaction mediated by gluons. The nucleus is very small, only about 1/10000 of the diameter of the atom.
Maybe electrons and quarks also have an inner structure, but this has not been scientifically confirmed. In an extension of the Standard Model, the so called String theory, the smallest objects are supposed to consist of very small strings and not of particles.