The Brazil international completed his protracted transfer between the two clubs earlier this month when his £198m release clause was triggered.
Barca attempted to dig in their heels to prevent one of their star men from departing, while La Liga chief Javier Tebas also stepped in at the time, but they proved powerless as Neymar became the world's most expensive player.
However, the biggest transfer saga of the summer has now taken another twist as Barcelona are seeking €8.5m in damages, linked to the payment handed over to the player as part of a renewal bonus when he signed a new contract last year.
A statement on the Catalan club's official website read: "FC Barcelona have sent a claim to be made against Neymar for breach of contract to the RFEF (Spanish Football Federation) for it to be passed on to the French Football Federation [FFF] and FIFA.
"In the demand, the club claims back money paid as part of a renewal bonus based on the fact he has not fulfilled his contract. The amount is €8.5m in damages, plus an additional 10% in interest. The club also claims that PSG subsidise the amounts in the event that the player cannot take responsibility.
"FC Barcelona have taken these steps in order to defend their own interests after Neymar rescinded his contract with the club just a few months after signing a renewal until 2021."
Neymar, who put pen to paper on a fresh five-year deal at Camp Nou in 2016, has started life in Ligue 1 in style by scoring three goals and assisting three more in his first two appearances.