  In this article, we study the distribution of index of Farey fractions which
was first introduced and studied by Hall and Shiu. We provide asymptotic
formulas for moments of index of Farey fractions twisted by Dirichlet
characters for Farey fractions with $\mathcal{B}$-free denominators.
Additionally, we reconsider the squarefree case earlier done in [ALVZ08], and
obtain new results for moments of indices with square-free denominators. We
also study higher level correlations of the index function generalizing earlier
known results on two level correlations.
