Pufferfish is a delicacy in some places. You can get in on the “eat dangerously, die satisfied” mindset in Stardew Valley if you use the right bait and fish in the right spot.
Pufferfish are ocean fish, and they can only be caught on the mainland during the Summer. However, for every other season, they can be caught on Ginger Island. This means that you’ll be fishing from the beach on the mainland, or Ginger Island’s Pirate Cove, or South, Southeast, and Western shores.
If you’re in need of a Pufferfish and it isn’t Summer, you can also use Magic Bait which let’s you catch any fish regardless of the season.
The Pufferfish can be a bit tricky to catch as they tend to move up and down quickly as if they’re bouncing in the water. You might want to use a Trap Bobber for Pufferfish to make it less likely that they’ll escape while you’re trying to reel them in.
You can also sometimes find them in garbage cans during the Summer, for some reason. And, like many things, it is sometimes for sale at the Traveling Cart for 600 to 1000 G.
Once you have a Pufferfish, you can turn it into sashimi. It can also be used as an ingredient in Quality Fertilizer and Maki Rolls. It also can be used as part of the Specialty Fish Bundle in the community center fish tank.