We know the composite subatomic particles are made up of odd number of quarks (at least 3 for baryons ) or combination of quarks and antiquarks (mesons). My question is if they don't exist individually in nature and also can't be seen using any apparatus how is this confirmed
You are asking about deep inelastic scattering.
Originally, neutrons and protons were thought to be the same particle, the only difference (other then EM charge and mass) was called isospin.
Protons and neutrons behave almost identically under the influence of the nuclear force within the nucleus. The concept of isospin, in which the proton and neutron are viewed as two quantum states of the same particle, is used to model the interactions of nucleons by the nuclear or weak forces.
Before the concept of quarks were introduced, particles that are affected equally by the strong force but had different charges (e.g. protons and neutrons) were treated as being different states of the same particle, but having isospin values related to the number of charge states. A close examination of isospin symmetry ultimately led directly to the discovery and understanding of quarks, and of the development of Yang–Mills theory. Isospin symmetry remains an important concept in particle physics.
So originally, isospin was introduced to explain the symmetries between protons and neutrons.
Deep inelastic scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons, muons and neutrinos. It provided the first convincing evidence of the reality of quarks, which up until that point had been considered by many to be a purely mathematical phenomenon. It is a relatively new process, first attempted in the 1960s and 1970s. It is an extension of Rutherford scattering to much higher energies of the scattering particle and thus to much finer resolution of the components of the nuclei.
Scattering means in your case a lepton being deflected. Inelastic means that the target absorbes some energy. At high energies, the nucleon get shattered, into pieces, quarks, but they are not actually falling into quarks, because of the quarks confinement. Deep means that the lepton energy is high, short wavelength, so it can probe distances that are small compared to the size od the nucleon.
In particle physics, hadronization (or hadronisation) is the process of the formation of hadrons out of quarks and gluons. This occurs after high-energy collisions in a particle collider in which quarks or gluons are created. Due to colour confinement, these cannot exist individually. In the Standard Model they combine with quarks and antiquarks spontaneously created from the vacuum to form hadrons.
It is very important to understand that quarks can only exist in confinement, that is why this is called hadronization.