There are right-handed anti-neutrinos but no right-handed neutrinos.
The “left-handedness” or “right-handedness” refer to the chirality of a fermion. Elementary particles with spin=1/2 are known as fermions. Neutrino is a fermion because it has spin=1/2.
Chirality is different from helicity. The best explanation of these concepts was given by Philip Tanedo. You should read Tanedo’s excellent tutorial.
I want to emphasize that chirality is a quantum mechanical property of elementary particles. It is a property of the quantum mechanical wavefunction.
Left-handedness of neutrinos is the key to the mysteries of elementary particles. Explanation of the left-handedness of neutrinos will be a breakthrough.