Fanjingshania is the earliest jawed fish known, at 439 million years old of the lower Silurian, and could be to be a member of the group which placoderms (and all other jawed fish) emerged from.

However, we believe placoderms and all other fish (the ancestral group which would later become cartilaginous fish, acanthodians ("spiny sharks"), and bony fish, had already diverged at this point, and likely did so during the Ordovician.

There is an outside possibility that Fanjingshania is a member of that basal population, from which all other fish groups came (and, therefore, all vertebrates) but this is looking unlikely, as it's too late and already carries features giving it affinity with the acanthodians, which have no living relatives.

A 2016 study found all cartilaginous fish to be more closely related to acanthodians than any other group and recovered acanthodians as stem-chondrichthyes, while another group in 2012 had found acanthodians to not actually exist and assigned all its members either to Chondrichthyes (cartilaginous fish) or to bony fish.

Most taxonomists at the moment seem to be agreeing with the acanthodians as stem-chondrichthyes model.

Additionally, working out how these swam was very important because these had the earliest pelvic fins. Vertebrate legs emerged from pelvic fins. It can give clues into the later evolution of tetrapods.

TL;DR; This is probably a member of an early divergence from the lineage which resulted in vertebrates, not an ancestor of vertebrates itself.