What are associated anti-particles?
Sometimes scientific writing can get a little dense. But in this case, it doesn't really mean very much. You probably read it in a context like this:
"Photons from the particle accelerator beam interact with lead shielding to create electrons, muons, neutrinos and the associated antiparticles."
Every particle has an antiparticle. They are identical in every way except for their charge. A positron is the antiparticle of an electron and carries a positive charge. The antiproton is the antiparticle of a proton and carries a negative charge.
In the interaction described in the quote above, particles and antiparticles are produced in pairs. The energy of the photon can become mass. When an electron is created, a positron is also created. That's all that is meant by associated antiparticles.