  Let $L/F$ be a quadratic extension of totally real number fields. For any
prime $p$ unramified in $L$, we construct a $p$-adic $L$-function interpolating
the central values of the twisted triple product $L$-functions attached to a
$p$-nearly ordinary family of unitary cuspidal automorphic representations of
$\text{Res}_{L\times F/F}(\text{GL}_{2})$. Furthermore, when $L/\mathbb{Q}$ is
a real quadratic number field and $p$ is a split prime, we prove a $p$-adic
Gross-Zagier formula relating the value of the $p$-adic $L$-function outside
the range of interpolation to the syntomic Abel-Jacobi image of generalized
Hirzebruch-Zagier cycles.
