It sounds like you have a possible name and place, and you are just not sure exactly who the father was? As opposed to just -- there *must* be a father, but you nothing except the surname the kid was born with?
If it's more like the former, then I identified my mother's 2x-great-grandfather Van Meter with good certainty using her autosomal DNA test. I knew my great-grandmother's probably main ancestor with her surname,and I knew her father was John Van Meter. But I didn't know which man of that name, so I couldn't determine the line down to her.
I created a big spreadsheet with every match I could find who had a tree showing a Van Meter in the same general family (starting by searching the match list for people with Van Meters in their trees, including variant spellings, then looking at the shared matches with those matches to find a few more even). In many cases, I noted errors in their trees and had to fix them with reference to land and probate records, etc.
Once I had a couple dozen names or so with the correct lines identified, there was a pretty clear pattern with the closest matches mostly descending from one guy (named John!), the next most distant matches descending from his father, and the next most distant from *his* father. It was fun partly because I'd have a close match who seems to descend from the most distant ancestor, but then I'd find a mistake in their line and it would turn out they are a closer relative. That happened a few times. It was also fun because the man I identified as the 2x-great-grandfather was not someone I had looked at before -- he lived mostly in PA, and I was expecting NJ, so I hadn't really explored the PA records well.
There's an image of the spreadsheet on the profile of the man I identified as the 2x-great-grandfather:
https://www.wikitree.com/wiki/Van_Meter-861
I actually have a few more rows in my local copy of that sheet, so this reminds me to update the image.
