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Let (A,\mathfrak {m}) be an excellent normal domain of dimension two containing a field k \cong A/\mathfrak {m}. An \mathfrak {m}-primary ideal I is a p_g-ideal if the Rees algebra A[It] is a Cohen-Macaulay normal domain. If k is algebraically closed then Okuma, Watanabe and Yoshida proved that A has p_g-ideals and furthermore product of two p_g-ideals is a p_g ideal. Previously we showed that if k has characteristic zero then A has p_g-ideals. In this paper we prove that if k is perfect field of positive characteristic then also A has p_g ideals. [ABSTRACT FROM AUTHOR]