I have a light switch that has the black wire attached to the bottom terminal and the white wire attached to the top terminal. Is there any way I can add another light switch for recessed lights to this circuit?
This sounds like a switch loop. What this means is the power for the lights is delivered to one of the lights and then this wire breaks the hot to turn the lights off, to add more lights using this circuit you would need to pull another line to that switch box and feed the new lights from the existing hot , neutral and ground. If you have attic access to the wiring it would not be two hard, without access you would need to open the walls / ceiling to run new wires. It can be done but is a lot more work for the second switch and new fixtures.