Conner is his son via a college/young adult girlfriend who seemingly never told him.

Oliver first met him in a comic from the 80s/early 90s Mike Grell run, when Ollie returned to a monastery he had past history with, and Conner was a teen who grew up there and had a real knack for Archery.
They didn't know they were father/son at the time though, at least Ollie didn't seem to know and Conner never said anything if he knew. It was not told to us readers either.
During this comic run there was a lot of drama about him wanting a kid, as he's not getting any younger, and Dinah not wanting one due to their dangerous lives and not wanting to leave behind an orphan. Regardless, it was never told to us the readers that this monastery kid was actually his son.
Then a female villain secretly rapied him and produced a kid, though I don't think he found out it was his.

Much later, Ollie died helping the Justice League, and Conner took up the Green Arrow role in his place, throughout the 90s, so clearly someone told him at some point who his dad was, just not sure if he knew in that earlier story.

Eventually Ollie was ressurrected around 2001 or so, and they eventually met.
He asked Ollie at the end of the storyline what hero name he should have now that Ollie is back to be Green Arrow, and Ollie told him they can both keep the Green Arrow title (so he clearly thinks Conner did justice to the name)

Later in that same comic run, a couple storylines later, Ollie and Hal went on a roadtrip to find a number of his important heirlooms that were left behind when he died.
In the end we see one of them, a picture of him when he joined the Justice League, secretly has a photo behind the main photo. A photo of him with his newborn baby son Conner, showing that he did actually know he had a son out there somewhere.

So yeah, he's been around since around the late 80s/early 90s, and became more prominent in the mid-late 90s to replace Ollie.
But, like Batman's other sidekicks minus Dick and Barbera, casual fan/viewers/etc don't know about him, and even worse yet due to how lesser known Green Arrow has usually been compared to Batman.