What can i do about my cousin going on my Xbox and getting me banned for a year

Anything that happens on your account is your responsibility. Saying someone else in your home (or wherever your console was at the time) used your account is not going to be enough of a defence. There is no way for Microsoft to know it wasn't you anyway.

You can appeal on the enforcement site, https://support.xbox.com/en-GB/help/family-online-safety/enforcement/enforcement-history

Not this account got ban it my old account is permanent is banned about 3 years go and this my new one and it got ban for 4 days for trash talk then I realise what I doing wrong then I stop doing it

I game share with my cousin we typically take turns buying games. So now in order to use the games i bought on my perma banned account i need to log in and set it as home xbox so i can get the games. Would me logging in give me another console ban ?

Hi there Dorian welcome to the community forum! Christopher here, an Xbox fan just like you and has been on Xbox for years already. I would really love to make your day by helping you out. From personal experience (my cousin also got permanently banned) I can tell you that, unfortunately, there is no way to get your account back, only the enforcement team is capable of removing the ban, and it seems they decided to keep your account banned. I'm sorry about the situation.