Hutch takes to wearing a large ring with a flat, green-ish stone setting during the second season. The ring was David Soul’s own, according to some sources a gift from his then girlfriend Lynne Marta (see e.g. S&H UK monthly magazine, issue 23, page 26). You can see him wearing it in his post-S&H works, too, such as Salem’s Lot. It is an impressive piece of Native American jewelry, either Navajo or Zuni. The UK magazine mentions the design has not only turquoise but also jet in it, but it’s hard to find a good, sharp close up of the stone. The more I look at it, an intricate turquoise/malachite/coral/opal/jet inlay wouldn’t be impossible.
This is the best photo I’ve found so far:
I think the ring first appears in 02-18 “Survival”, although there it looks like David Soul just forgot to take it off: Hutch doesn’t have the ring when he hurts his finger while cooking, but it’s on him when he drives out to the supposed meet. Then, the ring disappears for the duration of Hutch’s ordeal in the canyon, only to reappear in the tag. In “Survival”, Hutch wears it on his right ring finger, but he often switches it to the left hand (not sure, but it might be on his index finger sometimes, too).
The ring comes and goes for a while, but becomes a signature piece of jewelry for Hutch by Season 3; by Season 4, you rarely see him without it.
EDIT 2020-01-01: Just noticed the ring makes a blink-and-you-miss-it appearance in 01-16 “The Hostages”, when Hutch pushes the strap of Sweet Alice’s dress up her shoulder. It’s only seen in that brief close-up, Hutch doesn’t wear it elsewhere in the episode. It’s possible David had it on during an early take when they were still rehearsing, but the clip worked so well they included it in the final edit (as Pat Ackor suggests here).