A legal action taken by Paul Marriott, a former director of the company, International Natural Energy, also seeks to have it wound up.
The case taken by Mr Marriott represents the latest bout of feuding within the company since it discovered massive reserves of crude oil in Belize in 2005.
Another former director, Jean Cornec, is taking legal action seeking millions of euro he claims are owed to him after he sold his shareholding.
INE was founded by two women from Northern Ireland, Susan Morrice and Sheila McCaffrey, along with Mr Marriott, Mr Cornec and Mike Usher, who has since died.
Most of its 400 shareholders are Irish people who at one time attended one of Mr Quinn’s “Educo Mind Power” seminars. Mr Quinn was not involved when oil was discovered, but was invited to join the board two years later.
Subsequent disagreements among directors led to the suspension of Ms McCaffrey, who is currently considering her legal options.
While most shareholders remain fiercely loyal to Mr Quinn, a minority have expressed frustration at the lack of financial information from the company and its failure to pay a dividend since oil started flowing.
INE earns up to $100 million in oil revenues each year but says it has had to borrow heavily to fund further exploration and is prevented by its banks from paying a dividend.
Last Christmas, it provided $9 million in loans to shareholders who were “in good standing” with the company. Mr Marriott, through his drilling company Maranco LLC, has started his legal action in the High Court in Nevis, the Caribbean offshore tax haven where INE is incorporated.
The claim is against INE and its subsidiary Belize Natural Energy, Mr Quinn and Ms Morrice.
He is seeking a court order compelling the defendants to purchase his shares or else to liquidate the company.
He is also seeking a declaration that the purported appointment of Mr Quinn as a director be declared null and void.
In a letter to shareholders, Ms Morrice says Mr Marriott’s claim is “wholly without merit” and part of an orchestrated campaign against the company. Shareholders will “lose everything” if the case is successful.
“In the world, throughout history, the tail always seems to wag the dog.
“Similarly here, a small minority are loud and aggressive about their position while the silent majority just looks on.”
Mr Marriott then responded with his own letter to shareholders, in which he states that liquidation of the company is being sought “as a last resort”.
Last week Mr Marriott told The Irish Times his action would help other “poor souls”, many of them Irish, who had put money into the venture.
While a liquidation wouldn’t be helpful to anyone, “if it gets to that, so be it”.
Mr Quinn could not be contacted for comment.
SIC: IT/IE