Is "quasi planet" habitable for life?

I was imaging a system which has a black hole, a star and Earth like planet. The star and planet orbits around the black hole, but the planet has same orbital period as the star, which is a "quasi planet" of the star (see:this, at this case, the Earth is replaced by the star and the quasi satellite is replaced by the planet). Is this planet habitable for life?

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Is "quasi planet" habitable for life?

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