The branch in question appears to be what is called a "sucker," which is vigorous growth emerging from the roots or rootstock at the base of a tree trunk. In this case, your nectarine is probably grafted onto roots of a different tree (probably another nectarine, peach, or relative) for various reasons; it is a standard practice among fruit tree producers. Letting the sucker continue to grow will deprive the nectarine of resources (water, nutrients) and if it fruits, its fruit will not be what you expect. Therefore, we recommend removing it before it develops any further. For the future, suckers are best removed when young. Prune this one off with sharp pruners or loppers (or a folding pruning saw if you do not have loppers), cutting close to the trunk but avoiding cutting into the trunk itself. A stub of about a quarter to half an inch would be good so the wound seals over properly. Make sure the stub isn't covered with mulch so it stays dry.
Going forward, here is some advice regarding nectarine tree pruning for general tree health and productivity: https://extension.umd.edu/hgic/topics/training-and-pruning-stone-fruit.