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In the paper we consider three state p-adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the p-adic Gibbs measures to the solution of certain recursive equation, and using it we will prove that a phase transition occurs if and only if p = 3 for any value (non zero) of interactions. As well, we completely solve the uniqueness problem for the considered model in a p-adic context. Namely, if p ≠ 3 then there is only a unique Gibbs measure the model. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]