This looks to me like you have double vertices, i.e. several vertices in the same location, making two corners of that face loose. How you got those double vertices I can't say for certain, but most likely a mistake during extrusion. To check, go into edit mode, select that face and move it away slightly to see if something like this happens.
If it does, restore it to how it was before you pulled the face away, by hitting CtrlZ as many times as needed, then select everything by pressing A as many times as needed.
Then for 2.80 hit CtrlV followed by M then B to merge vertices by distance, i.e. merge vertices that are close to each other.
For 2.79 hit CtrlV followed by D (if I remember correctly, some builds used R instead of D), to remove doubles.
You'll need to do this before beveling.
The following should appear in the lower left corner of your Blender window, to let you configure the distance by which to merge vertices. If the dialog is closed, open it be clicking the little arrow to the left of the title "Merge by Distance". Leaving it at the default will likely be fine. This is for 2.80. Unfortunately I don't have a 2.79 install, but a similar dialog should appear if that's the version you're running.