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How big is your turtle? A little less than an inch long.
How long have you had it? 2 weeks.

What is the water temperature? 78 degrees.
Are you using a water heater? Yep.
How much water is in there? Around 75% full.
Are you using a water conditioner? Nope.
Are you using any filtration? Yes.

What is the basking temperature? 96 F.
Is there a basking light? Yes.
Is there a basking platform that is easy to climb on? Yes.
What kind is it or what is it made out of? ZooMed Turtle Dock.
Is there a UVB light? Yes.

What have you been trying to feed it? Lettuce and Pellets.
When was the last time your turtle ate? Around a week ago.

How big is the tank/pond/enclosure? 60 Gallons.
Is the tank near a window? No.
Is the tank in a room with a lot of activity? No.

Have you read the Basic Care section? Yes.
Have you searched the forums for similar situations? Yes.

Is there any other unusual activity/symptoms? Frequent basking, not eating (possible RI), black, soft spots on the shell.

I've had the little RES for about two weeks now, bought him along with another small cooter (that's doing fine right now) and put them with a 4-inch RES.

The big one hasn't harmed any of them, but sometimes hogs the food.

The cooter's been eating well, but the small RES hasn't. In recent days, the RES doesn't eat even when I place a piece of food up right in front of it, and basks a lot.

What I'm most worried about is the black spot on the shell, though. It looks chipped when dry, and looks as though it was burnt (I don't think the basking lights could've done this, as my other two have been fine basking under those lights). It's significantly softer than the rest of the shell, being flexible. I don't think it's shell rot, though, because from the pics I've seen, shell rot is not black.

All help is appreciated.

Welcome to the forum.

The size difference between the little one and the bigger RES is too great. I'd separate little RES and give him his own set-up, with the water temp several degrees warmer (81-82F) until he's closer to the size of the largest turtle (and then you will need a much bigger tank/container for them). How big is the cooter?

It sounds like there's too much competition in the tank for food and the little one is losing out. Can you feed him separately? Try some smelly food (look on the site for info on getting a reluctant turtle to eat).

The basking area temp is a bit too high. I'd lower it to around 90F.

A pic of the damaged area of the shell when it's dry would be helpful.

If in spite of your efforts the little one refuses to eat and/or you start seeing other symptoms, your turtle should be seen by a herp vet.

I agree with Marisa. It may also be that the little one is on the basking platform more because he is nervous in the water. With a size difference like that, the smaller turtle is easily intimidated by the larger, which can cause stress and illness, as well as not eating. If you seperate him from the others and the symptoms continue, a trip to the vet is called for. The bigger turtle could kill the little one, even by accident, so it really would be best to seperate them as marisa said.