A fourth law firm has objected to its share of common benefit fees in the transvaginal mesh litigation, insisting that lawyers tasked with distributing the $550 million fund failed to compensate it for work in a critical New Jersey trial.

Bernstein Liebhard, based in New York, joins three other law firms that have objected to their allocation of common benefit fees, which are designed to compensate lawyers for work that had a “common benefit” to all the litigation over transvaginal mesh devices. More than 100,000 lawsuits were filed over the devices, most of them coordinated in multidistrict litigation in federal court in West Virginia. But one of the first trials in the nation was in New Jersey’s Atlantic County Superior Court, where one of the defendants, Johnson & Johnson’s Ethicon, lost an $11 million verdict in 2013.