Przytycki and Sokolov proved that a three-manifold admits a semi-free action of the finite cyclic group of order
p
p
with a circle as the set of fixed points if and only if
M
M
is obtained from the three-sphere by surgery along a strongly
p
p
-periodic link
L
L
. Moreover, if the quotient three-manifold is an integral homology sphere, then we may assume that
L
L
is orbitally separated. This paper studies the behavior of the coefficients of the Conway polynomial of such a link. Namely, we prove that if
L
L
is a strongly
p
p
-periodic orbitally separated link and
p
p
is an odd prime, then the coefficient
a
2
i
(
L
)
a_{2i}(L)
is congruent to zero modulo
p
p
for all
i
i
such that
2
i
>
p
−
1
2i>p-1
.