Kim Zolciak was spotted out in public for the first time since losing primary physical custody of her kids ... amid her ongoing legal battle with Kroy Biermann.

The "Real Housewives of Atlanta" reality star kept her look casual but still luxe ... rocking an all-black designer outfit.

She sported a fitted long-sleeve crop top, joggers and Balenciaga slides while moving through her day.

The Bravolebrity was seen taking phone calls while running errands around town ... and later in the day, she was snapped picking up her kids from school.

It seems she's keeping things low-key during the outing as attention around her personal life continues to build.

We broke the story ... Kim has temporarily lost custody of the kids she shares with Kroy -- the latest twist in their messy legal battle.

A judge had ruled on Kroy's emergency motion and gave him primary physical custody of the kids. The 'RHOA' alum will have limited parenting time with their 4 minor children every other weekend.

Kim and Kroy will continue to share joint legal custody of the children, but Kroy has final decision-making authority regarding educational, non-emergency medical, and religious decisions.