The Brazil forward left the Nou Camp this month for a world-record £200.6million, joining Paris St Germain in a move that more than doubled the previous highest fee.
Neymar signed a contract extension with the Catalan giants in October previous year before leaving for Paris earlier this month in a €222 million deal.
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 past year.
The amount is €8.5m in damages, plus an additional 10% in interest.
The Brazilian ace has netted three times from his opening two Ligue 1 games as PSG have enjoyed a goal-laden, flying start.
He notably scored twice and provided two assists on Sunday evening during his home debut against Toulouse.
Barcelona said the suit was filed on August 11.
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The demand appears to relate to a payment made to Neymar when, in 2016, he renewed his contract with Barcelona through to 2021.
Barcelona continue to express their public disagreement after the player paid the buy-out clause to end the contract unilaterally.
In a statement released on Tuesday, Barca said they had passed the complaint on to the Spanish Football Federation (RFEF), having first filed the lawsuit in a Barcelona court on August 11. "The club also requests that PSG subsidise the amounts in the event that the player can not take responsibility".
"FC Barcelona has started these proceedings to protect its interests following Neymar's decision to buy out his contract just months after he signed an extension until 2021".
"To see my former teammates unhappy makes me sad also, because I have many friends [there]".
"I had four very happy years there, but Barca deserve much better".
"I do have something to say, that I am disappointed with them [Barcelona directors]".