Welcome, and sorry for your father's passing.
Here is a good post for revolver ID information:
To IDENTIFY your Gun >
You have a .38 Double Action that likely dates to the mid-1880 decade. It uses the .38 S & W round, shorter and fatter than the .38 Special; the latter will fit diameter-wise but will not fully seat. Ammo is still available online and should be safe if the gun is mechanically sound.
The barrel appears to have been shortened, unless there is a bunch of patent information stamped on the right barrel (the side not visible in the photo) or everything is legible on the top strap. Hard to tell if it has been refinished, but if so someone did a nice job. Hope this is helpful