  We construct generic Gelfand-Tsetlin representations of the $\imath$quantum
groups $U_q^{\text{tw}}(\mathfrak{so}_3)$ and
$U_q^{\text{tw}}(\mathfrak{so}_4)$. These representations are
infinite-dimensional analogs to the finite-dimensional irreducible
representations provided by Gavrilik and Klimyk. They are quantum analogs of
generic Gelfand-Tsetlin representations constructed by Mazorchuk. We give
sufficient conditions for irreducibility and provide an upper bound for the
length with the help of Casimir elements found by Molev, Ragoucy, and Sorba.
