Can this planet in a binary star system exist?

In a certain star system, Star B orbits Star A. Planet C lies in between the two stars and also orbits Star A. Planet C and Star B share an orbital period, and are at roughly the same places in that period. Consequently, there is no night on Planet C. As Star A sets, Star B rises.

Is such a configuration possible (and if so, plausible)? Could such a planet support life, or would the constant exposure on both sides to radiation make the planet too hot?

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Can this planet in a binary star system exist?

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