Depends. Varied state to state. In free states they were granted citizenship.
Constitutionally they were supposed to be denied citizenship. Even the Indians were explicitly excluded. Lincoln was to send them home to avoid today's mess.
The first legally recognized slave owner in America was black. Very likely blacks and Jews disproportionately owned the majority. Contrary to the propaganda, European whites leaned toward indentured servitude over straight up slavery. At least with that you had contractual terms and conditions with an agreed finite period. As such, still retained many rights. For example, rape could be breech of contract and children were not born into slavery.
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