What or how do you claim anexemption for bank account frozen jointly?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

You have to prove that the funds in the account are exempt or not generated by you.

You have to go to the court that issued the order to freeze the account, and present evidence that the money in the account ( or what percent) belongs to the other person. Deposits slips that match pay chekcs and so on.