An heir to the fallen Barneys luxury empire got served with an explosive tax-fraud lawsuit from his estranged brother — while he was in the middle of promoting his gossipy new memoir last week at a New York City bookstore, The Post has learned.

Gene Pressman, 74, was signing copies of his new book, “ They All Came to Barneys: A Personal History of the World’s Greatest Store ,” at Rizzoli Bookstore in Manhattan last Tuesday when he got a nasty surprise, according to a source briefed on the encounter.

A so-called “process server” — a professional hired to hand court documents to defendants — had bought a copy of the fashion-infused tome and stood in line with other fashionistas to get it signed by Pressman, sources said. 6

But when it was his turn to step up to the table, instead o

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