Please see the attached .pdf or .jpg diagram for ease of discussion... First, the house wiring is very old and there are only 4 wires in the switch box (2 black, 2 white & no bare ground wire). "Scenario A" currently uses only 1 of the 2 duplex switches to turn on both light fixtures. It doesn't matter if you use top or bottom duplex switch to turn on BOTH the recessed downlight and the Hunter light/fan fixture. As for the fan, the fan and light are independently controlled by using the 2 pull chains (1 pull chain for fan and 1 for 4 light globes). We commonly use 1 chain pulled ON so fan lights are ON when the switch is thrown. This way BOTH of the 2 independent light fixtures come on when entering the kitchen when either of the 2 duplex switches is turned on. How would I wire Scenario B single pole Wifi smart switch to existing 4 wires (2 black and 2 white) to make the 2 fixtures light? Whoever wired the existing Scenario A switch was able to make it work with a single pole switch since the tab has not been broken between the 2 common screws and it only takes one of either of the 2 switches to be thrown to make both fixtures to light up. If you do break the tab off between the 2 common screws, the two lights now work independently using one switch or the other. Is it possible to wire this up using a single pole switch (Wifi switch or not) and have both fixtures light up? There must be an electrician out there that can successfully understand how Scenario A is currently wired and answer this puzzling question. Again, please see the attached diagrams for ease of discussion. Thank you for your help and insight in advance!

 

You new switch requires a neutral. You don't have one. It appears you have two switch loops.
I would bet if you cut the tab the lights would be controlled independently by the switches. You can do a test by removing one of the black wires and see if only one light comes on.

 

Thank you for the reply JoeD! You are correct, if you break the tab between the two common screws the lights would indeed illuminate and be controlled independently by the switches. So do you know if there is any type of WiFi Smart Switch that can be used to operate this kitchen switching configuration? If there is the possibility of using a WiFi switch, what would the WiFi Smart Switch be called? Example, single pole, 3-way, double pole double throw etc.? Of course keeping in mind there are only 2 black, 2 white and no common ground wires pulled to this switch box. Thank you for your help and for sharing your knowledge!

 

I do not know all the brands and features. You need to find one that does not require a neutral or a ground. Check the specs of the switches.

The other option is to pull in a new cable with power and neutral.

 

Lutron makes a few that don't need a neutral but they require a bridge.
The link below is to a site where the options are explained pretty well.

Smart switch without neutral

 

Thanks PJmax and joed! Appreciate the info!