I am currently in Naples as a crew member onboard a ship and due to disembark soon to return home to South Africa.
Is it possible to apply online or at an embassy here in Naples for a Schengen visa in order to travel Europe?
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The general rule is that Schengen visas cannot be issued at the border.
However, there are special exceptions from this (Schengen Visa Code, article 36 and annex IX) for seamen who leave service on a ship in a Schengen port and need to transit the Schengen area to return to their home country.
Such a visa must be arranged through the shipping company (who has to make certain guarantees) -- contact your employer ASAP and let them manage the paperwork.