Not really since you still seem to be mixing and matching but I will try.
Party A has sued party B in Federal court for payment of work that was never performed and has third partied C in claiming party C received the benefit of the alleged work.
Since there is no Federal question then there has to be diversity and the amount has to be over 75,000. I assume that both of those are present.
Party B answers claiming the work was not performed. This is a pure contract question.
Party C answers denying the claim they received any benefit or that they were never a third party beneficiary of the contract and then files for summary judgment after discovery.
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