  In this paper, we consider the Potts-SOS model where the spin takes values in
the set $\{0, 1, 2\}$ on the Cayley tree of order two. We describe all the
translation-invariant splitting Gibbs measures for this model in some
conditions. Moreover, we investigate whether these Gibbs measures are extremal
or non-extremal in the set of all Gibbs measures.
