What document should I submit to US immigration services to prove my income from university as a teacher assistant is legal?

Tax returns and W-2 forms. A letter from the school would also be helpful, and it should include a statement that your position was part-time and performed on campus, as allowed by your visa - if that's the truth, of course. That is the only type of acceptable work done under an F-1 visa.

if you were employed on CPT or OPT enclose copies of the authorization or EAD card.

Proof of income documents as stated by other attorneys, if you had authorization to work.