The Nova Scotia Supreme Court was to consider the application made by his widow Jennifer Robertson on behalf of the company.
Quadriga CX announced mid-January that Cotten died of complications from Crohn's disease on December 9 while volunteering at an orphanage in India. He was 30.
In an affidavit cited by Canadian media, Robertson said the company has been unable to access on its main computer the cryptocurrencies owed to 115,000 users.
"I do not know the password or recovery key," Robertson said. "Despite repeated and diligent searches, I have not been able to find them written down anywhere."
The company's digital platform allows trading of Bitcoin, Litecoin and Ethereum.