"for my paper" is correct and usable in written English.
It could be used in a sentence such as: "I researched extensively for my paper on ancient civilizations."
"Billy would design dresses for my paper dolls".
"I already have a little paper box for my paper clips".
"I called Bob Hughes, one of the people who wrote for my paper".
"This," he was heard to remark, "will be good for my paper".
It was raining, so I asked for a plastic bag for my paper.
I am standing in line at the train station one morning, waiting to pay for my paper.
"I was not speeding, I was not asked for my papers, I was just put in custody for several hours for no reason," he said.
"I just want to be able to use the women's room and not have someone ask me at the door for my papers," she said.
We were just chatting and when I asked what he thought of Damascus, he said, 'Oh, I just went for my papers, the problem with Arabs is that they don't have a culture'.
A young Spanish man who is a member of an ethnic minority group put it this way: "I worry when I go on the street that the police will stop me and ask me for my papers because of the colour of my skin, or my way of walking".
