  It is known that $A$-paths of length $0$ mod $m$ satisfy the Erd\H{o}s-P\'osa
property if $m=2$ or $m=4$, but not if $m > 4$ is composite. We show that if
$p$ is prime, then $A$-paths of length $0$ mod $p$ satisfy the Erd\H{o}s-P\'osa
property. More generally, in the framework of undirected group-labelled graphs,
we characterize the abelian groups $\Gamma$ and elements $\ell \in \Gamma$ for
which the Erd\H{o}s-P\'osa property holds for $A$-paths of weight $\ell$.
