  In this paper we address the existence of time periodic solutions for the
generalized inviscid SQG equation in the unit disc with homogeneous Dirichlet
boundary condition when $\alpha\in (0,1)$. We show the existence of a countable
family of bifurcating curves from the radial patches. In contrast with the
preceding studies in active scalar equations, the Green function is no longer
explicit and we circumvent this issue by a suitable splitting into a singular
explicit part (which coincides with the planar one) and a smooth implicit one
induced by the boundary of the domain. Another problem is connected to the
analysis of the linear frequencies which admit a complicated form through a
discrete sum involving Bessel functions and their zeros. We overcome this
difficulty by using Sneddon's formula leading to a suitable integral
representation of the frequencies.
