What's the full puzzle that goes like Person A Never lies Person B Always lies Person C I don't remember.. Then they all say what they have and it continues like Person A says that person B is lying Person B says that person C is wrong
As the comments have mentioned, I believe the puzzle is most commonly called knights and knaves, with knights always telling the truth and knaves always lying.
There are many variations from the original, however.. Ranging from adding other types of behaviors (e.g.. random), having multiple characters give testimonies and you have to guess who's lying and who's telling the truth, etc. For these kind of questions you can check the liars tag in this SE.
I believe it's going to be very difficult to pinpoint a specific version unless it's one of the original ones - there's like hundreds to thousands of liars puzzles out there.