People who work at Kate Quinn, a fashion brand that specializes in clothes for children and babies, say they feel like hiding under their desks whenever a new collection goes on sale.

They’re joking, but not really.

On drop days, the staff finds itself slammed with web orders for the latest ruffled onesies, tiny cardigans and soft swaddling blankets. After a new collection sells out, often within minutes, a vibrant resale market springs up on sites like Mercari and Facebook Marketplace, where Kate Quinn clothes and accessories fetch dollar amounts many times the original retail price.

Rachel Red-Horse, a teacher in Hawaii who discovered Kate Quinn a few years ago, said that shopping for her two young children has become a retail blood sport. “It’s all a game of who has the fastest internet,” she said.

Thriving online markets are typical for things like Supreme box logo sweatshirts and Hermès handbags, not baby clothes. But for some parents Kate Quinn is almost impossible to resist. On social media, fans of the brand have formed groups to show off their hauls, complain about what they can’t get and bond over their attempts to resist yet another shopping spree.

Ms. Red-Horse and other parents interviewed for this article praised the quality and sophistication of the designs, noting the brand’s emphasis on organic cotton and bamboo. And unlike the garish or utilitarian stuff sold by other baby clothes companies — pink for girls, light blue for boys — Kate Quinn’s offerings include refined items like ruffle-bum leggings with a pattern of garnet wisteria and tops that come in gender-neutral hues with special names (“twilight mauve,” “pearwood,” “honey bee,” “thyme,” “graphite,” etc.).

When a collection is released, Ms. Red-Horse, 27, said she typically logs on right away and moves fast to click on what she wants. A crucial stretch comes at checkout time: If she is not quick enough, she said, she risks getting “cart-jacked” — that is, watching in horror as her selections disappear from her cart when another shopper beats her to payment.

Ms. Red-Horse said she got a glimpse of the secondary market for all things Kate Quinn while searching for a certain crib sheet with a whale print. After finding that it was sold out on the brand’s website, she put out a request on a buy/sell/trade group and was soon bombarded by baby-clothes flippers.

“I had people offering me things for $70 when they retail for $40,” Ms. Red-Horse said. “Another mom said, ‘I bought two sleep sacks for $800 in that print.’ They’re $45 brand-new!”

Kate Quinn is not an overnight sensation. The company started in 2006, when its namesake founder started selling kimono-inspired wrap onesies on Craigslist. At the time, Ms. Quinn had no children. Her experience in the apparel industry was scant — a year at Fashion Institute of Design & Merchandising in Los Angeles and some time working as a wardrobe stylist for photo shoots.

Her brand got a boost when Nordstrom and a few upscale children’s clothing boutiques started carrying it. Things really took off in 2018, when Ms. Quinn decided to sell directly to customers online, which allowed her to cut prices by half. Instead of offering new designs for each season, she started putting out limited themed collections, released as drops.

Ms. Quinn, 44, who now has two children and lives north of Seattle, said her love of vintage wallpaper and luxe interiors has informed her designs more than fashion. And she counts herself among those stupefied by the frenzy over her products.

She noted that one of her most popular items, the Kate Quinn quilts, did not sell very well at first. “That turns into, everybody wants a quilt,” she said. “People were sending us pictures of quilts on Mercari for $800. It was shocking.”

During the past two years, her company has bolstered its website and hired dozens of employees while dealing with pandemic-related supply-chain issues and shutdowns at its factory in India. It has also put limits on the number of quilts a customer may purchase, while quadrupling the supply of popular items like ballerina bubbles, a bodysuit with side skirts.

The measures were not quite enough to contain the frenzy. “During the pandemic, we really were just holding on for dear life,” said Paul Weinstein, the brand’s chief operating officer.

Ms. Quinn said she had no plans to slow the drops, either. Rather than make more of popular older styles, the company is releasing close to 50 collections a year, she said. Speaking of her customers, Ms. Quinn said, “I think they would rather be delighted by something new.”

Some of the brand’s loyalists become disappointed, even furious, when they are unable to buy what they want. Ms. Quinn said she decided to leave Facebook after a few customers posted personal details about herself and her family, including her home address. In a guarded tone, she said, “It got a little intense when customers couldn’t purchase the bubble or quilt of their choice.”

Rachel Semple, a 27-year-old mother of a baby, said the low prices and stream of new styles have helped spur what she described as “FOMO frenzy shopping” for Kate Quinn products.

“It’s comical,” she said. “But it’s insane. It’s legit people’s lifestyle.”

Ms. Semple, a third-grade teacher in Knoxville, Tenn., added that she has given up on trying to buy prints that are especially in demand, like the beluga whale pattern that appeared on pants, jumpers and quilts last year. “I find the ugly print that no one wants, just because it’s not stressful,” she said.

And Kate Quinn seems to hold its value.

“In a purge, I can make $200 in one night,” said another fan of the brand, Tayler Landry, 29, who lives in Michigan and has an infant daughter. Someone offered her $250 for a little body suit, an offer Ms. Landry turned down because it made her feel uncomfortable, she said.

Many Kate Quinn shoppers are new mothers, and the brand becomes part and parcel of the life-changing event of becoming a parent. Some devotees take part in online “camo” contests — posting photos of their offspring dressed in a patterned Kate Quinn bodysuit while lying on a matching Kate Quinn quilt. (Where’s the baby?)

Chermae Peel, 40, a college administrator and mother of three in West Texas, said she met three mothers who had daughters born the same time as hers on a website for Kate Quinn fans. “We’d take photos and make a collage,” she said. “That’s what Kate Quinn was for me. It brought all the moms together.”

“It was clothes,” Ms. Peel continued, “but more so it was the friendship.”

The brand started expanding into women’s and men’s clothing over the past two years, and more recently into the tween category. Now the whole family can match.

For anyone caught up in the Kate Quinn shopping craze, Ms. Peel had some advice: Stay levelheaded. And be patient.

“My daughter loves elephants,” she said. “I wanted a quilt. Well, someone was selling an elephant quilt in a ‘buy, sell, trade’ group. Sure enough, I waited, and I was able to get the quilt. We survived.”