IN HIS INTRODUCTION to a recent anthology, Great Esquire Fiction, L. Rust Hills, the magazine's fiction editor, credits his predecessor Gordon Lish with founding the New Fiction. Since Hills doesn't define this category beyond singling out two exemplars reprinted in the anthology--William Kotzwinkle's hilarious "Horse Badorties Goes Out" and T. Coraghessan Boyle's wicked "Heart of a Champion"--let me try my hand. In a time of egregious turmoil (1969-77), these and dozens more stories published under Lish's imprimatur offered rude, gab- drunk, disorienting, fearful alternatives to mainstream magazine fiction. It was a period when John Cheever wrote a story narrated by a human belly but Esquire was there first, a period when many a story-lover weaned himself from the front of The New Yorker.

Since leaving Esquire, Lish has served as an editor at Knopf and busied himself with writing his own fiction, which looks rather New. Last year he published his first novel, Dear Mr. Capote, a tour de force about a maniac bent an assassinating the perfect master of publicity and prose. His new book draws together stories written over the last seven years.

Many of the New fictions rely heavily on outlandish suppositions, some of these not far removed from the "What If" segments of the original Saturday Night Live. In "Heart of a Champion," for instance, the premise is that Lassie has a sex life. The trick (by which I mean art) is to extend such potent donn,ees full length without sacrificing spontaneity to design.

"For Jerom,e--with Love and Kisses," the longest story in Lish's collection, belongs to the "What If" school, and it's a lulu. As the title indicates--by punning on J.D. Salinger's "For Esm,e--with Love and Squalor"--the story is a send-up of America's second most elusive literary hermit. (You might try to identify numero uno as we move along.) The premise is that Mr. Ess, J.D.'s widowed father, a resident of Miami's Seavue Spa Oceanfront Garden Arms and Apartments, has some bones to pick with his famous son and sits down to write a kvetching letter.

For one thing, Jerome has just changed from one unlisted phone number to another without notifying guess whom. Has the son's obsession with privacy gone so far as to freeze out his sole surviving parent? If it's reached that stage, Mr. Ess might as well do himself in. "One miniwink," he writes, "and your father will be only too happy and glad to make you a present of his own dead body."

Next there's this "J.D." stuff. Why has the son ditched his perfectly good Jerome David? It so happens that the Seavue Spa and Soforth is chock-a-block with literary kinfolk, and Mr. Ess has a hard time facing them these days. "Like take, for instance, a certain Mrs. Roth who lives in this building. So tell me, darling, does she have a relation who is a Philip or a P? Or look instead at the Bellow people who got such a nice oceanview on 10. Ask yourself, do they a have a second cousin named Saul or a seond cousin named S? The Malamuds on 6, a one-bedroom facing front, we're talking in this case about a Bernard in the family or a B?" Mr. Ess' trump card is to warn that the King of Sweden--now we're talking Nobel Prize--will think "you didn't have the heart to put your whole name down."

One more thing and Mr. Ess will shut up. Would it cause Jerome all that much pain to go on television like every other famous writer, just once? "Pussycat, what will it cost you to pick up the phone and tell Merv you'll make an exception?"

As I hope these quotations have suggested, what crowns the piece with glory is Mr. Ess' acrid, self-lacerating, guilt-dispensing tone. He's the most spellbinding Jewish complainant since Stanley Elkin's "Bailbondsman" raised his voice in outrage, and the story is a classic screed. (Still pondering who our most secretive writer might be? A hint: in a flight of fancy, Lish has transformed him into a Jewish son who infuriates his mother, another Seavue denizen, by Anglicizing his given name: Thomas Pinkowitz.)

Among the 17 other stories, I marked half-a-dozen for rereading some rainy day--not a bad percentage as story collections go. One of these, "For Rupert--with No Promises," augments Lish's debt to Salinger by purporting to extend the Glass family saga. "Guilt" is an affecting story of an emotion that needs no foundation in fact. "Frank Sinatra or Carleton Carpenter" memorable depicts the bogies that plague earnest parents. "Fear: Four Examples" is notable if only for a wonderful phrase: the narrator suffers from a "rogue cramp."

Other stories in the collection are irritatingly obscure. Owing to the excessive archness of their narrative voices, they manage to fall on their faces and make the reader feel clumsy. No matter. "For Jerom,e--with Love and Kisses" alone is reason enough for you to buy Lish's book --and for J.D. to mend his ways.