Unlikely intersections between isogeny orbits and curves

Fix an abelian variety $A_0$ and a non-isotrivial scheme over smooth irreducible curve, both defined the algebraic numbers. Consider union of all images translates fixed finite-rank subgroup $A_0$, also numbers, by subvarieties codimension at least $k$ under isogenies between some fiber scheme. We characterize curves inside which are dominate base curve potentially intersect this set in infinitely many points. Our proof follows Pila-Zannier strategy.