Hi, could anyone tell me how to express the following idea correctly?

The claim doesn’t seem prevalent/right/correct/true/apply under any circumstances or indeed something else that I’ve not even thought of?

Does “something else that I’ve not even thought of” refer to some other circumstance beyond “any circumstances”? If so, I don’t see why you need to say it at all. Could you not just say:

“The claim doesn’t seem right/correct/true under any circumstances.”