It's clear that you're not talking about humans here, but I'm going to use human hands as the basis for my answer, as they are by far the most relatable hands for me personally.
I would definitely say they'd come out from in between the fingers. For one thing, there's actually space in between the metacarpals for claws to rest. The hands would however need to be a little wider to account for the claws as well as new muscles whose primary function is moving the claws, and a little fatter to account for the curvature of the claws.
Second, if there were to be a retractable claw coming from a fingertip, the final knuckle of that finger would need to be longer than the claw in order for there to be room for it to fully retract, assuming it actually can fully retract. Because if the retracted claw extended into the second knuckle, the fingers wouldn't be able to bend well, which would severely limit fine manipulation. On my fairly average-sized hands, a 2 to 2.5-inch claw could fit comfortably in between my metacarpals, but only a half-inch claw in my fingertips. For comparison, lions have roughly 1.5-inch claws, and tigers have roughly 4-inch claws. Since the primary function of claws in cats is grasping, these longer claws are very useful to lions and tigers because they lack fingers. Human fingers are already pretty good at grasping things, so a short claw at the end of a fingertip may be sufficient for most human claw-related needs. But longer claws in between the fingers would allow the fingers to rest, even when climbing or hooking prey, so they wouldn't be tired later when it's time to do a task requiring fine manipulation. On a related note, you would definitely want claws on a fingered hand to be able to extend while the fingers are extended for two reasons. One: For increased grasping capability. And two: Imagine trying to climb a tree with balled-up fists. There's no way your claws would reach the tree and you'd scrape your knuckles on the bark.
Third, human fingers contain no muscle tissue; only fat and connective tissue. If a finger were to sheathe a retractable claw, it would need to be a massive bratwurst finger in order for there to be room for a bone, fat, connective tissue, a claw, and muscles to hold the claw in place. And depending on how long you want the claw to be, the final knuckle of each finger would need to be very long. One possible solution to this would be to have the final knuckle of the fingers not have a bone, and instead only be a skin flap covering a claw. The skin flap could recede over the previous knuckle to reveal the claw. Theoretically this motion could be make with no muscles in the fingers, using only connective tissue connected to muscles in the hand. It doesn't sound very structurally sound to me, though.