  The PTOLEMY experiment, implementing a $100~{\rm g}$ surface-deposition
tritium target, is promising to detect cosmic neutrino background via $\nu^{}_e
+ {^3}{\rm H} \to {^3}{\rm He} + e^-$. In this talk, I consider a thermal
production of right-handed Dirac neutrinos in the early Universe, and
investigate their impact on the capture rate of cosmic relic neutrinos at
PTOLEMY.
