Writing letter of recommendation for someone I have never met I'm a first year PhD student. A student applying for an undergraduate institution in the US has asked me to write him a letter of recommendation. I wonder if a first year graduate student can write recommendation letters to high school graduates applying to US colleges.
This is not my main question though. That student has a connection to my family. I discussed physics with him once and I wasn't able to form any idea about his physics ability. What's worse, he wants me to recommend his friend who is also applying to US colleges, although I have never met or spoken with his friend at all. He wrote himself a recommendation (which I have to send as if it's I who had written it) that he had worked with me in the physics laboratory and that he was my strongest student. I wish to know how to proceed. I have two options:

refuse to write that letter

write that I have never met him.


I wonder how common is this.
You shouldn't write a letter of recommendation for someone you have spoken to once, and you certainly shouldn't write a letter of recommendation for a friend of some you have spoken to once.
You should never lie in a letter of recommendation, but it is generally also bad form to write negative things in a letter of recommendation. If you can't in good faith write good things about a candidate, you should refuse to send the letter.
EDIT:
I'll add an answer to your first (not main) question from the comments:
It is very unusual for a first year grad student to be asked to write a letter of recommendation, particularly since he is asking you to say he is your best student, when presumably you have no students. If I were the admissions tutor here, I'd probably disregard such a letter. Unless it was obviously dodgy (claiming things which were clearly untrue), in which case, it would count (heavily) against the candidate.