Schinoussa is one of the Small Cyclades, the cluster of low islands between Naxos and Amorgos. It is small enough to walk across, with a hilltop village, a handful of sandy coves and very little traffic, and it attracts people who want a slower few days after the crowds of Paros. Getting there from Paros is the natural move if you are working your way east through the Cyclades.
The link between the two islands runs on the larger ships that serve the Small Cyclades. Our route data lists Blue Star Ferries, which sails a conventional car ferry on this line, and Seajets, but we do not hold a sampled timetable for this direction and Ferryhopper does not publish a route page for it. That means we cannot confirm which days a direct boat sails, and we would not assume it is every day.
You leave from Parikia, the capital and main harbour of Paros, and arrive at the small port below the main village of Schinoussa. There is no large hotel scene on the island, only rooms and small guesthouses, so book your bed first and then find the boat that fits.
If the direct sailing is not on your date, go via Naxos. Paros to Naxos is one of the busiest short hops in the Cyclades, and from Naxos the local Express Skopelitis of Small Cyclades Lines and larger ships continue to Schinoussa. Leave a comfortable buffer between the two legs and check that both run on the same date.