ground cover found in upstate SC, tiny round leaves, red stems. Grows flat to the ground. Seems perennial. Average moisture in soil, Intense afternoon sun. Might have tiny flowers, but none seen this summer.
the plant in the picture is most likely the Cranberry Cotoneaster, Cotoneaster apiculatus. It is a popular prostrate shrub used as a ground cover. It is not native.
I hope this helps.
Steve Hill, Botanist, SCNPS