The retired physics teacher I am married to had a student claim that his copy of the test didn't have a certain page in it. The triangle of paper left when he tore the page out was left under the staple.
There is always the classic kid who was told to use a pencil on his test (not Scantron) had written on the top of his page "Reason for pen, no pencil." The person who copied his test very carefully wrote the same on his test, in pencil.
My husband also had two versions of each test, often with completely different questions in certain places and often with just different numbers in the problems. I did his typing for him and was very careful to make them look the same at a casual glance, except of course for the tiny number at the bottom that indicated the version, and there were only a few differences anyway. He caught a lot of copiers that way, and the kids learned a lesson to not try it again. (It also was nice that all the kids got to review the varying questions at review when the tests were returned.)
He also had a student scheduled to take a makeup exam after a legitimate absence. The kid came storming into the office saying that this wasn't the same test Jason had taken. Husband said "No, but it covers the same material." The student threw the test down, said, "Well! I might as well just not take the test then!" and stormed out.
There were very strict safety rules in the science department. Each student was required to bring in a copy of the contract, signed by himself and a parent. Students who violated the rules were not allowed to take the class that day. Every year a few parents would come in whining about the kid's being kicked out, so the teacher would just go to the file cabinet and pull out student's contract. He never had trouble from special snowflakes, but some kids really got into trouble with their parents for forgery.
Some girls were stooped below the desk setting pieces of paper on fire, just for the fun of it! We never did figure that one out, but it was known they couldn't work together when the Bunson burners were turned on.