  We consider a gas of repulsive $N$-component fermions confined in a
ring-shaped potential, subject to an effective magnetic field. For large
repulsion strengths, we work out a Bethe ansatz scheme to compute the two-point
correlation matrix and then the one-particle density matrix. Our results holds
in the mesoscopic regime of finite but sufficiently large number of particles
and system size that are not accessible by numerics. We access the momentum
distribution of the system and analyse its specific dependence of interaction,
magnetic field and number of components $N$. In the context of cold atoms, the
exact computation of the correlation matrix to determine the interference
patterns that are produced by releasing cold atoms from ring traps is carried
out.
