Those are probably primary ballots; in New York (and some other states), they only let you vote in primaries for candidates of the party that you're registered in (and if you're registered independent, you don't get to vote in the primary at all). The general election ballot will have all parties on it.
I’ve only received republican ballots and my cousins have only received democratic ballots. He wants to vote for trump but it’s not on his ballot
Those are probably primary ballots; in New York (and some other states), they only let you vote in primaries for candidates of the party that you're registered in (and if you're registered independent, you don't get to vote in the primary at all). The general election ballot will have all parties on it.
Good to know. Thank you!