I am renovating a bathroom and need to add an exhaust fan with a separate swich from the light. There are three wires coming into the switch box, red, black, and white. The red goes to one side of the switch. The black goes to a wire nut for an exiting light and another black comes from that wirenut and goes to the other side of the switch. The white goes to the white from the existing light. I have added 12/2 romex, two pieces from the new fixture. The neutrals will go together in the switch box. Does the power come from the red of the black?

Is the power source for these switches at the outlet in the ceiling? Or does power come to the switches and then to the fixture?

This is critical to know since switches do not use a Neutral Connection, unless they have a pilot light that requires a Neutral.

Any chance you can attach pictures of what you are trying to do?

Also, if the circuit is a 15 amp circuit, then you would use a 14/2 cable, not a 12/2 cable (20 amp).