No - there has never been a submarine with that name in the current or past Naval fleet. The only ship to bear the name Poseidon was USS Poseidon, (ARL-12), an Achelous-class repair ship in WWI.
There was a movie, USS Poseidon: Phantom Below, which had a fictitious Navy submarine called the Poseidon. However, the hull number is for the active commissioned submarine USS Georgia (SSGN 729), and there has never been an attack submarine with that hull number or designation.
Hollywood rarely uses real hull numbers of active ships to avoid any legal problems. The exceptions are those in which the production involves ships/submarines in which the storyline actually involves them. For example, The Hunt for Red October featured the USS Dallas, a real LA-class fast-attack submarine, of which an old friend of mine served aboard during filming. Usually though, the film will use a decommissioned hull number - many older films use 593, the hull number of the Thresher, which sank in the early 60's.
The submarine you are thinking about was the USS Nautilus. It was the world's first nuclear powered submarine and commissioned into the US Navy in 1955
Navy
submersible boat
The Hunley sank with all hands after its attack.
The USS Nautilus (SSN-571) was the US Navy's first nuclear powered submarine.
He was an Irish Engineer who created the first submarine commissioned by the US Navy, and the first for the British Navy.
Royal Navy Submarine Museum was created in 1963.
The Trieste is now housed at the U.S. Navy Museum on the grounds of the Washington Navy Yard in Washington, D.C.
$2.4 billion for the newest Virginia Class attack submarines
Royal Netherlands Navy Submarine Service was created in 1906.
The submarine was USS Redfish (SS-395).
The Ohio Class ballistic missile submarine at 560 feet in length.