I found this in my grandfather’s barn where I had inherited a 1904 Soderfors anvil and forge a few months before. I’m not sure what it is. Not a regular Blacksmithing hammer. The handle hole in my opinion is too small for a striking handle. I would guess it is just for a holding handle like a top fuller or punch. I have two - one is a 3lb and one is a 3 1/2 lb. one of them has a touchmark, but I can’t make out what it is. Any help would be appreciated. 

I agree.  The photos appear to show a Altha ( well worn touchmark of a horseshoe surrounding the capital letter A) top fuller or possibly a well used hot or cold cut tool (or maybe even a stone cutter?).  I would vote for a fuller that may have been changed over the years, due to the second mark on the top that appears to be a dimension (often the radius of the end of the fuller - in this case perhaps 1/4"?  Definitely a "struck" tool of some flavor designed to be used with a smithing team of striker and director.  With a little bit of creativity these can be modified to be used as a variety of top tools, even if that wasn't the original purpose.

I'd lean towards stonecutter's hammer, of which Atha was a major manufacturer. In that case, it would be swung solo, and not be a struck top tool. 

I'd go with a stone hammer too.

On further research, stone hammer seems more likely, but not sure why you feel it would necessarily be a solo tool in that case.  Here are a couple that clearly show signs of being hit by sledges.

   

Because a lot of them were (as I understand it) swung by hand. 

I've seen records of these in sizes from around 2.5# up to 14#.  I expect the larger ones were swung by hand, solo,  but not the smaller ones like in the OP.  Could certainly be wrong...

Stone sledge or mason's hammer.  The same pattern has come up before on this site.  Here's an old "Iron City" ad with similar but there were variations by manufacturer

Thank you very much. That answers two of my posts. The mason’s hammer and cross pein sledge. Awesome!

When cutting stone to size, a one hand sledge can be used to strike the mason hammer, thus the signs of that kind of usage.

Yes, that is exactly what I was describing.  The earlier post used "swung solo" to differentiate the use from that of a struck tool.