  We study the gauge dependence of the one-loop effective action for the
abelian $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory formulated in
harmonic superspace. We introduce the superfield $\xi$-gauge, construct the
corresponding gauge superfield propagator, and calculate the one-loop two-and
three-point Green functions with two external hypermultiplet legs. We
demonstrate that in the general $\xi$-gauge the two-point Green function of the
hypermultiplet is divergent, as opposed to the Feynman gauge $\xi =1$. The
three-point Green function with two external hypermultiplet legs and one leg of
the gauge superfield is also divergent. We verified that the Green functions
considered satisfy the Ward identity formulated in ${\cal N}=(1,0)$ harmonic
superspace and that their gauge dependence vanishes on shell. Using the result
for the two- and three-point Green functions and arguments based on the gauge
invariance, we present the complete divergent part of the one-loop effective
action in the general $\xi$-gauge.
