How do I add an independently controlled light fixture to an exiting three way circuit?
I believe this is what you are requesting:  the new light must always be off when the original light is off but can optionally be turned on while the original light is on.

To accomplish this you can connect the new light in parallel with the original light, but with a switch on the hot leg, like this:



Or use a new light that has a built-in pull-chain, which is a switch that will accomplish the same thing.

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