  In this work we provide an asymptotic expansion for the Szeg\H{o} kernel
associated to a suitably defined Hardy space on the the non-smooth worm domain
$D'_\beta$. After describing the singularities of the kernel, we compare it
with an asymptotic expansion of the Bergman kernel. In particular, we show that
the Bergman kernel has the same singularities of the first derivative of the
Szeg\H{o} kernel with respect to any of the variables. On the side, we prove
the boundedness of the Bergman projection operator on Sobolev spaces of integer
order.
