Adding a switch to a light circuit
There are a couple of ways to do what you want.

The gist is basically intersecting the spot light but allowing the power to not be interrupted when the existing switch is turned on.  Simple enough.  I've added two possible scenarios of how it might be wired.   The spare neutral is required by code, but only if the ceiling is closed off and not accessible.  It can be capped or taped off inside the switch box.