  In this work we use the modified replica trick, proposed in arXiv:2205.01150,
to compute the late time behaviour of complexity for JT gravity with ${\cal N}
= 1$ and ${\cal N} = 2$ supersymmetries. For the ${\cal N} = 1$ theory, we
compute the late time behaviour of complexity defined by the ``quenched
geodesic length" and obtain the expected saturation of complexity at time $t
\sim e^{S_0}$, to a constant value with time-independent variance. For the
${\cal N} = 2$ theory, we explicitly compute complexity at the disk level which
yields the late-time linear growth of complexity. However, we comment on the
expectation of the late-time saturation by speculating the trumpet partition
function and the non-perturbative corrections to the spectral correlation,
relevant for the late-time behaviour of complexity. Furthermore, we compute the
matter correlation functions for both the theories.
