According to a new lawsuit, obtained by TMZ, Rudolph is suing Ronald over the rights to "The Isley Brothers" trademark ... he says Ronald applied and got approval for the trademark in his own name and is taking all the profits.

Rudolph says he and Ronald are supposed to split all profits from the band 50/50 ... claiming they've each had 50% ownership in the band since their brother O'Kelly died way back in 1986 ... but Rudolph claims Ronald recently went rogue.

In the docs, Rudolph claims Ronald applied for and was granted the exclusive rights to "The Isley Brothers" for use on "visual recordings and audiovisual recordings featuring music and animation" back in August ... but Rudolph says Ronald needs his approval to cut such a deal.

Rudolph says Ronald applied to put the trademark in his name in November 2021 ... but Rudolph claims they previously split all the profits for some big transactions, including a multi-million dollar publishing deal ... and now he wants the judge to order an accounting to see just how much money Ronald's been raking in since the change.

What's more, Rudolph wants the court to step in and declare "The Isley Brother" trademark is jointly owned by him and his brother ... and he wants Ronald to cough up half of any money he's been making off their band's good name since getting the trademark.