You can create an offset between Constrained and Source objects using the translation offsets found in the Properties window.

To offset the Constrained and Source objects in a Path constraint:

1. Double-click the constraint in the Scene browser to select it.
2. Open the Properties window. The Path constraint settings display.
3. Expand Path Settings > Offsets > Translation offset and set a value in the Roll, Pitch, or Yaw fields for the desired effect. See Offsets for more information on roll, pitch, and yaw.