Dannà is a Neapolitan dialect word that means "damn me" or "condemn me." It's a strong, dramatic verb that you don't often hear in everyday Italian, making it quite unique and memorable.
In the context of "Resta cù 'mme," the singer uses it to express the depth of his desperation and willingness to endure any suffering for his beloved. He pleads, "Famme dannà, ma dimme sì" (Damn me, but tell me yes), highlighting his intense desire for her to stay, even if it means eternal torment. This powerful emotional plea makes the word particularly striking.