Can a Cohen marry a woman whose mother is Jewish but not her father? What are the sources?

A Cohen may not marry such a woman, as written in the Shulchan Aruch, Even Haezer section, Siman 6, that a woman that had marital realations with a Gentile, she and her daughter are forbidden to marry Cohanim. This is not a punishment to the Cohen - it's recognition of his being on a special level and showing his importance. Rabbi Ro'i Margalit