In order to study p-adic etale cohomology of an open subvariety U of a smooth proper variety X over a perfect field of characteristic p > 0, we introduce new p-primary torsion sheaves. It is a modification of the logarithmic de Rham-Witt sheaves of X depending on effective divisors D supported in X - U. Then we establish a perfect duality between cohomology groups of the logarithmic de Rham-Witt cohomology of U and an inverse limit of those of the mentioned modified sheaves. Over a finite field, the duality can be used to study wildly ramified class field theory for the open subvariety U.