According to the text and the Fifteenth Amendment to the Constitution of the United States, states cannot deny a person the right to vote for the following reasons:
- on the basis of race
- on the basis of having been enslaved
The text specifically mentions that the right to vote shall not be denied on account of race, color, or previous condition of servitude.
The other options, "on the basis of citizenship" and "on the basis of gender," are not covered by the provided text regarding the specific prohibitions of the Fifteenth Amendment. The Nineteenth Amendment addresses voting rights regarding gender, but it is not part of the text you provided.