There's quite a bit of missing details there. Is there any reason to suspect that this family had connections to Ireland at all? Are there any indications that any members of this Barnes family ever went to Ireland? To get from 1630 to 1713 you have to cover a lot of ground in wills and property records. That should be where you start. What happened to all the property? I expect you will find that this family died out in the male line.