America’s Food Basket supermarket on Geneva Avenue will close this month and will be replaced by a new supermarket operator with deep roots in Dorchester. The Slawsby family, which operates four Save-A-Lot supermarkets in Greater Boston, plans to renovate and upgrade equipment in the Fields Corner space over the next few months.

It is not yet clear whether or not the new operators will re-open under the name Save-A-Lot. The transition follows a four-year-long legal battle in which America’s Food Basket appealed control of the space. Having lost its final appeal, the New York-based chain will vacate the roughly 20,000 square-foot space in the coming days.

Jonathan Slawsby, 44, and his brother Todd, 50, run the Save-A-Lot stores with their father, Harold, 82, from a headquarters in Brockton. They will be the third generation of Slawbsys to operate a supermarket in the Fields Corner shopping center, which is owned by Supreme Realty Trust, which in turn is managed by Tom Cifrino, whose family has also owned and managed Dorchester stores for generations.

Cifrino confirmed on Tuesday that America’s Food Basket would vacate the space by Feb. 1, allowing the Slawsbys’ contractors to begin work on a renovations that should result in a new-and-improved store opening, with a target date of May 1.

This will be the second major transition in the Fields Corner mall in 2020. Target will open its second Dorchester store in the shopping plaza this spring. The retail giant will fill a void in the mall that was left when the discount clothing retailer Fallas closed its doors in November 2018. Target is currently in the middle of a complete renovation of its 27,000-square-foot space to accommodate its store.

Target operates similar “small-format” stores in Roslindale and Brookline. The other Dorchester Target — in the South Bay Mall— is much larger, at roughly 100,000 square feet.

Jonathan Slawsby says that his family’s company is familiar with operating successfully in close proximity to Target, which will also sell groceries.

“They approach food differently,” he said, noting that the Save-A-Lot stores are known for high quality meats and perishables. “Our format is to get the best quality product and the best prices to the community. We’re hoping to help — along with Target— bring a fresh approach to the shopping center.”

The Slawbsys currently operates three other stores, on American Legion Highway in Roslindale, Martin Luther King Boulevard in Roxbury, and on East Ashland Street in Brockton.

“We’ve always wanted a store in Dorchester and we’ve looked high and low,” Harold Slawsby told the Reporter in a 2015 interview. “I’ve known the Cifrinos for many years. In fact, they outbid us for that [Fields Corner] land in the 1950s. But we’ve always been friendly competitors and stayed closed to the family.”

The Slawsby family’s experience in Fields Corner dates back to the 1940s. Harold Slawsby’s father ran a meat market at 1498 Dorchester Ave., a precursor to the Capitol chain that his family later opened. In addition to the Fields Corner location, the family operated stores on Morrissey Blvd.— a building that now houses a liquor store and a CVS— and at Morton Street and Gallivan Boulevard, a site now occupied by Norfolk Hardware.

“I grew up basically in Fields Corner in ‘46-‘47 in my father’s store,” said Harold Slawsby.

Today, there is another vacancy in the Fields Corner mall: Payless Shoes closed last year. Cifrino said that he is currently looking for a new tenant for that space.