Adjacent light circuit is inadvertently controlled by four-way switch wiring
I don't believe you have four way switches. Four way switches do not have commons as they do not control the light directly, they simply break the path of two other three ways. Three ways have 3 screws, four ways have 4. (And the ground)

Next, (to answer your question) since the exterior light only works when one of the switches are on, most likely you've connected to the final wire feeding from the switches to the light. I believe this imagine below will help you out:



Basically, you use 3 way switches coming from the power source and then leading to the light. Then you can use an infinite amount of four way switches between these two. 

Since you can control your light from 3 locations, but this location has 3 screws - this switch is a 3 way. Now it's just finding out if it's either the first or the last. If it were the first, connecting to the common would give you what you want. However, you've most likely tied off from the last switch leading to the light and so it only works when the overhead light works. There is no way to split off power from the current location and work as you desire. You'll have to run another wire.