  Xue proved an equational refinement of the unitary Shimura curve case of the
arithmetic Gan-Gross-Prasad conjecture via the Gross-Zagier formula for
quaternionic Shimura curves. On the other hand, Rapoport, Smithling and Zhang
posed a variant of the conjecture, using modified PEL type Shimura varieties,
which we call RSZ Shimura varieties. We reinterpret the result of Xue in terms
of the modified Shimura curves. We then use the reinterpretation to prove a
case of the variant of the conjecture. Our result combined with the work of Xue
establishes a connection between the variant and the Gross-Zagier formula.
