  We extend the construction of upsilon-type invariants to null-homologous
knots in rational homology three-spheres. By considering $m$-fold cyclic
branched covers with $m$ a prime power, this extension provides new knot
concordance invariants $\Upsilon_m^C (K)$ of knots in $S^3$. We give
computations of these invariants for some families of alternating knots and
reprove some independence results in the smooth concordance group.
