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The port of Mergellina was the pier of neapolitan fishermen. Today it's used for connections with the Island of Ischia, the Pontine Islands and the Aeolian Islands; also for the mooring of yachts and sailboats that go around the Mediterranean.
Sea connections with hydrofoils (passengers only) are active only in the summer period. Those for Ischia are daily; those for the Pontine and Aeolian islands are instead surrounded on weekends.
However, the number of connections to Ischia is rather limited: if there's no valid reason to leave from Mergellina, it's better to do it from Molo Beverello or from Calata Porta di Massa.