Okay, so my boyfriend got a note that сказал(-а) nasty things on it and сказал(-а) that i wrote it. I told him I didnt write it, and he doesnt believe me. What should I do?

If he doesn't trust that Ты wouldn't say those things about him, that means he didn't trust from the beginning. Ditch him!

Say "If u dont have enough trust in me too believe that i didnt write that note. Then this relationship isnt going too work."
I know its hard to say something like that
But a good relationship is built on trust

Find out who wrote it, and improvise from there.

Either appeal to their better nature and get them to tell your boyfriend the truth, или just find another way to prove to him it wasn't you.

Break up with that bastard~

give him what he wants if Ты know what i mean