The salt presumed to contain Nitrate is mixed with newly created FeSO4 for a Ring test. BaSO4 has extremely low dissolvability at standard temperature and pressure and thus will precipitate as a white colored residue. If that residue stays in your test tube you will not go through with the test properly.
Although, the residue can be sieved out and the filtered solution will contain the free Nitrosonium Complex ([Fe(H2O)5(NO)]2+) which will provide us the ring test. A better framing for this question would be to ask “How it can be proved by a ring test that Ba(NO3)2 comprises of a nitrate ion?”. In subjectively analyzing a salt we might repeatedly need to isolate the precipitate if the salts do not comprise of the radical we needed to test by any method required.