  In this paper, we introduce the conception of Rota-Baxter paired comodules,
which is dual to Rota-Baxter paired modules in [14]. We mainly discuss some
properties of Rota-Baxter paired comodules, especially we give the
characterization of generic Rota-Baxter paired comodules, which has important
application for the construction of Rota-Baxter comodules. Moreover, we
construct Rota-Baxter paired comodules on Hopf algebras, weak Hopf algebras,
weak Hopf modules, dimodules, relative Hopf modules and Rota-Baxter paired
comodules. And then we finally introduce the conception of Rota-Baxter paired
Hopf modules by combining Rota-Baxter paired module with Rota-Baxter paired
comodule, and give the structure theorem of generic Rota-Baxter paired Hopf
modules.
