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The most literal interpretation is to build the quotient ring $(\mathbb{Z}/3\mathbb{Z})[x]/(x^p - x - 1)$:

sage: p = 3
sage: A.<x> = PolynomialRing(Zmod(3))
sage: B.<y> = A.quotient(x^p - x - 1)
sage: B.cardinality().factor()
3^3
sage: B.is_field()
True

Since $3$ is prime you can also replace Zmod(3) by GF(3).

If $x^p - x - 1$ is irreducible (for example for $p=3$) then it is a modulus for the field with $3^p$ elements:

sage: C.<z> = GF(3^p, modulus=x^p - x - 1)