When did Dumbledore know Harry was a horcrux? (Patreon)

Was it when Harry touched the ring in Half-Blood Prince that Dumbledore found out that Harry was a horcrux? He was saying something about they leave something or have some kind of magical remnant.  When I was editing the video it seemed like thats the moment (when harry touched the ring and it started spinning) Dumbledore realized what Harry was.  Is this right, or did Dumbledore know all along?

P.S. I did seem like the scenes in Snape's pensive memory was around that time as well.

Thanks guys!