In this paper, we consider some lacunar power series in Qp, where p is a prime number. We obtain some results about lacunary power series with rational coefficients for Um-number arguments in Qp. We determined whether the values of the considered lacunar power series belong to a certain field of algebraic numbers or to the set of transcendental numbers in Qp. Also, we find similar results for lacunary power series with p-adic algebraic coefficients.