Starsky wears two rings in his left pinky all through the show, one golden with some kind of knot, and another a braided silver band.
The rings are Paul’s – he wore them outside the show, as well as in other projects before and after “Starsky and Hutch”. To my knowledge, Paul has never told where the rings came from or what they signified to him. According to dedicated PMG fans, he stopped wearing them sometime after marrying Elizabeth.
In fanon, there’s rather wide agreement that the rings belonged to Starsky’s father, but nothing is ever said about their history in the show.
When using stunt guys/doubles, they rarely bothered to add this detail to the Starsky costume, so when you see Starsky in action without his rings, or close-up of his hand without them, it’s almost certainly a stunt guy/double. Sometimes, like in “The Action” when he switches the dice, you do see a close-up of “Starsky’s hand” with a different ring on it.
There is a small curiosity about the look of the rings in S4 (see the pictures below). In previous seasons, the silver and gold bands sit closely together, but in S4 (maybe already in late S3) there almost always seems to be a wider gap between the rings that doesn’t seem to be just shadows. I’ll keep looking for clearer close-ups before making any definite claims, but an additional ring, maybe a narrow bronze braid, wouldn’t be impossible.