  We propose a skein model for the quantum cluster algebras of surface type
with coefficients. We introduce a skein algebra
$\mathscr{S}_{\Sigma,\mathbb{W}}^{A}$ of a walled surface
$(\Sigma,\mathbb{W})$, and prove that it has a quantum cluster structure. The
walled surfaces naturally generalize the marked surfaces with
multi-laminations, which have been used to describe the quantum cluster
algebras of geometric type for marked surfaces by Fomin--Thurston [FT18].
Moreover, we give skein theoretic interpretation for some of
quasi-homomorphisms [Fra16] between these quantum cluster algebras.
