The compound sodium sulfate is made of sodium ion and sulfate ion.
The formula can be written as Na₂SO₄.
The cation present in this compound is Na⁺ and the anion is SO₄²⁻.
The compound barium sulfate is made of barium ion and sulfate ion.
The formula can be written as BaSO₄.
This compound contains the cation Ba²⁺ and anion SO₄²⁻.
From the above , we can see that both the compounds have common anion which SO₄²⁻
So, the sulfate, SO₄²⁻ is the common ion when sodium sulfate is added to a solution of barium sulfate