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I got this turtle from a street vendor a few days ago, and he's been very lethargic, hasn't eaten and overall just seems to be declining in health.
The top of his shell looks okay, but he looks like he has a visible spine (if that indicates some sort of health concern). The underside is what worries me. It's puckered with yellowing sides (see pic).
What's the cause of this? How do I help him recover?

He opens his eyes if I move him, but otherwise keeps them closed. Yesterday he crawled on my hands and seemed to be okay, but today he doesn't even bother retracting his legs even when I flip him upside down.

His water is at 28 degrees celsius so it's not a cold problem. I just feel like there's some illness before my purchase and I would like help identifying it and getting the right meds for a full recovery. He doesn't look like he has much time left D;

Thanks for your time!

Try keeping his water at a constant 28C. I'd also try to soak him in a solution of 50% water and 50% Pedialyte. Leave in some crumbled pellets, maybe he'll swallow some when he drinks water for a couple of hours. For meds, you'd need to see an actual vet, but I don't think there is much they can do for a hatchling. Also consider some live prey like minnows. If he sees it wiggle in front of him, he might want to eat it.

Unfortunately, turtles from street vendors are in very poor conditions. Sickness, injuries and lack of appetite usually come with them.

Thank you Steve for the advice. Does his shell look okay though? Any indications of specific bacterial infections or anything like that?

The shell looks fine, I can't tell if there is anything wrong visually.