Strange that it doesn’t have any markings at all.
Based on some of the clues I see, I am going to say that is is most likely a Prentiss from the early part of the 1900’s. The removable tapered pin that secures the swivel back jaw looks to be missing and I wouldn’t be surprised if the swivel jaw is locked up and no longer able to swivel. With some work, those can be freed up. Don’t use violence. Those are valuable vises with strong collector value but of course can be great user vises once they are serviced properly.
It’s great that you now have your grandfather’s old vise. Nice heirloom!