some modifiers can apply to part of a mesh via vertex groups, but not subsurf. For subsurf to be applied portions of a mesh would require n-gons or at least a very different approach. so No you cannot apply subsurf to only a part of a model.
What you have to do is put vertices close together to make sharp corners. In other words, you CAN have a cube that is subsurfed but still looks like a cube. So you won’t get perfectly sharp corners , but those are rarely realistic anyways.
However, the previously mentioned ctrl E method is a good suggestion. heres an example of ctrl e applied to half of a subsurfed sphere:
to do this, I inserted a sphere, added a subsurf modifier and put it at level 3, then I selected one half of the vertices and pressed CTRL+E and dragged my mouse to the right until the number at the bottom of the window said +1.000. If this doesn’t solve the problem, you’ll have to post a picture of what you’re trying to do.