Let X → P 1 X \to {{\mathbf {P}}^1} be an Abelian covering of degree m m over Q ( μ m ) {\mathbf {Q}}({\mu _m}) unbranched outside 0 0 , 1 1 and ∞ \infty . If the genus of X X is greater than 1 1 embed X X in its Jacobian J J in such a way that one of the points above 0 0 , 1 1 or ∞ \infty is mapped to the origin. We study the set of torsion points of J J which lie on X X . In particular, we prove that this set is defined over an extension of Q {\mathbf {Q}} unramified outside 6 m 6m . We also obtain information about the orders of these torsion points.