I believe this is The Battle of Long Island by Nancy Kress, as per this previous answer. It was originally published in the February-March 1993 issue of Omni magazine.
The protagonist is Major Susan Peters, a nurse stationed at an Army hospital on Long Island in the year 2001. Within a compound located in what used to be Prospect Park in Brooklyn, there's a wormhole of some sort (referred to as "the Hole"), which leads to the Battle of Long Island in the year 1776. At the beginning of the story, injured 18th century soldiers (referred to as "the Arrivals") have apparently been coming through the Hole for three months already.
Some relevant excerpts from the story:
"Major Peters! You're needed in Recovery! Quick!"
I leave my tent and tear across the compound at dead run. We have only three people in Recovery; one of the weird laws of the Hole seems to be that they seldom come through it if they're going to recover. Musket balls in the belly or heart, shell explosions that have torn off half a head. Eighty-three percent of the Arrivals are dead a few minutes after they fall through the Hole. Another 11 percent live longer but never regain consciousness. That leaves us with 6 percent who eventually talk, although not to us. After we repair the flesh and boost the immune system, the Army sends heavily armored trucks to move them out of our heavily armored compound to somewhere else. The Pentagon? We aren't told. Somewhere there are three soldiers from Kichline's Riflemen, a fieldgrade officer under Lord Percy, and a shell-shocked corporal in homespun, all talking to the best minds the country thinks it can find.
This time I want to talk first.
The soldier who has finally woken up is a grizzled veteran who came through dressed in breeches, boots, and light coat. It's summer on the other side of the Hole: The Battle of Long Island was fought on August 27, 1776. Unlike most Arrivals, this one staggered through the Hole without his rifle or bayonet, although he had a hunting knife, which was taken away from him. He'd received a head wound, most likely a glancing shell fragment, enough to cause concussion but, according to the brain scan, not permanent damage.
When the Hole first opened, there was wild talk of putting the medical staff in Colonial dress - "to minimize the psychological shock." As if anything could minimize dying hooked to machines you couldn't imagine in a place that didn't exist while being stuck with needles by people unborn for another two centuries. Cooler heads prevailed. I wear fatigues, my short hair limp against my head from a shower, my glasses thick over my eyes.
My first interview with Sergeant Edward Strickland, Connecticut Third Regiment, First Continental Army, takes place the next morning. He's been moved from Recovery to a secure bunker at the far end of the compound, although he still has an elevated temperature and the remains of dysentery. Even in a standard-issue hospital gown he doesn't look like a man from our time. It's more than just the broken teeth. It's something unbroken in his face. He looks as if ass-covering is as foreign to him as polyester.
"Sergeant Strickland," commands the Military Intelligence expert, Colonel Orr. Unseen recording equipment whirs quietly. "Tell us all your movements for the last few days, starting with General Putnam's fortification of the Brooklyn Heights works."
Strickland has apparently decided he is not enlisted in this Army. He ignores the colonel and says directly to me, "Where am I, Mistress Nurse?"
Orr nods, almost imperceptibly. We've rehearsed this much. I say, "You're in an Army hospital on Long Island."
"What date be today?"
"July 15, 2001."
I can't tell if he believes me or not. The fierce black eyes bore steadily, without blinking. I say, "What work did you do before you joined the Army, Sergeant?"
"I was a smith."
"Where?"
"Pomfret, Connecticut. Mistress . . . if this be the future, how come I to be here?"
"We don't know. Three months ago soldiers from the Battle of Long Island began to stumble into a city park out of thin air. Most of them died. You didn't."
He considers this. His gaze travels around the foamcast bunker, to my glasses, to the M-18 held by the guard. Abruptly, he laughs. I see the moment he refuses the idea of the future without actually rejecting it, like a man who accepts a leaflet on a street corner but puts it in his pocket, unread, sure it has nothing to do with his real life.