Who is the only person to recognize Carton in the prison? Why has this person been sentenced to death?
In Dickens's A Tale of Two Cities, Sydney Carton takes advantage of his extraordinary resemblance to Charles Darnay, count of Evremonde, to save him from death by taking his place in prison. To do this, he bribes his way into the prison, drugs Darnay and, having dressed him with his own clothes, calls the turnkey and asks him to see his "visitor" out, remarking on the fact that he is feeling faint. Such remark is meant to conceal the effect of the drug.
Before the execution, a young seamstress who had been in prison with Charles in La Force the first time he was arrested approached him and engaged in conversation with him. At the beginning, the girl believed she was talking to Darnay, but at some point during the conversation, she realized that her interlocutor was someone else.
The seamstress did not really know why she had been condemned to death, but she knew she had been found guilty of plotting against the new regime, and was resigned to her fate. Here is the scene that illustrates your question:
"Citizen Evremonde," she said, touching him with her cold hand. "I am a poor little seamstress, who was with you in La Force."
He murmured for answer: "True. I forget what you were accused of?"
"Plots. Though the just Heaven knows that I am innocent of any. Is it likely? Who would think of plotting with a poor little weak creature like me?"
The forlorn smile with which she said it, so touched him, that tears started from his eyes.
"I am not afraid to die, Citizen Evremonde, but I have done nothing. I am not unwilling to die, if the Republic which is to do so much good to us poor, will profit by my death; but I do not know how that can be, Citizen Evremonde. Such a poor weak little creature!"
As the last thing on earth that his heart was to warm and soften to, it warmed and softened to this pitiable girl.
"I heard you were released, Citizen Evremonde. I hoped it was true?"
"It was. But, I was again taken and condemned."
"If I may ride with you, Citizen Evremonde, will you let me hold your hand? I am not afraid, but I am little and weak, and it will give me more courage."
As the patient eyes were lifted to his face, he saw a sudden doubt in them, and then astonishment. He pressed the work-worn, hunger-worn young fingers, and touched his lips.
"Are you dying for him?" she whispered.
"And his wife and child. Hush! Yes."
"O you will let me hold your brave hand, stranger?"
"Hush! Yes, my poor sister; to the last."
You can see that she did not actually recognize Carton; she only sensed that the man she was talking to was not the one she had met before. Carton confirmed this, but never told her who he was.