Fort Clinch State Park main entrance is off of Atlantic Avenue out near main beach. You’ll need to pay an entrance fee, but then follow the park road all the way to the Fort. You can park on the east side and walk over to the beach or park on the west side and walk over to the beach. There are jetties on the west side which may hold more fish.
Use a bottom rig such as a Fish Finder rig or Carolina Rig, or a jig. You could also use a slip float to fish deeper, but with the current. The current here can be very strong! Even good swimmers may struggle on an outgoing tide so be careful about wading out too far. Be extra careful with kids.
There are restrooms up at the Fort, which is a hike from the beach. The beach is not handicap accessible.