Barcelona's complaint relates to Neymar signing a new contract through 2021 in October of past year, with the club hoping to recoup his "renewal premium" as well as €8.5m in damages and a further 10 per cent in arrears.
Barcelona continue to express their public disagreement after the player paid the buy-out clause to end the contract unilaterally.
However, after his world record €222m transfer to PSG went through, club spokesman Josep Vives confirmed the club would not be making the payment as Neymar had not fulfilled his contractual duties.
The Catalans are asking for an additional 10% payment due to a delay in their demands being met, after presenting Neymar with them on August 11.
It comes after Neymar threatened to report his former club to Federation Internationale de Football Association over their refusal to pay a loyalty bonus due to him this summer in light of his switch to PSG.
Barcelona have also withheld a €26m bonus due to Neymar for signing the renewal to his contract past year.
FC Barcelona has started these proceedings to protect its interests following Neymar's contract termination just months after he signed a contract extension until 2021.
Amid a strong start to his PSG career, Neymar ripped Barcelona's board Sunday in an interview with reporters. For me, they shouldn't be in charge of Barca. "I'm very sad with them", he said in quotes published by Football Espana. "Barca deserve much better, and everyone knows this".
Moreover, Barca urged PSG to pay the amount they are seeking if Neymar - who is reported to earn €30m after tax for the next five years in Paris - isn't able to meet their demands.