We continue to develop the program initiated in arXiv:1705.04679 of studying supersymmetric AdS3 backgrounds of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of theories with varying coupling. Imposing 2d N=(0,2) supersymmetry, we derive the general conditions on the geometry for Type IIB AdS3 solutions with varying axio-dilaton and five-form flux. Locally the compact part if spacetime takes the form of a circle fibration over an eight-fold Y8τ, which is elliptically fibered over a base M6. We construct two classes of solutions given in terms of a product ansatz M6=ΣxM4, where Σ is a complex curve and M4 is locally a Kähler surface. In the first class M4 is globally a Kähler surface and we take the elliptic fibration to vary non-trivially over either of these two factors, where in both cases the metrics in the total space of the elliptic fibrations are not Ricci-flat. In the second class the metric on the total space of the elliptic fibration over either curve or surface are Ricci-flat. This results in solutions of the type AdS3xK3xM5τ, dual to 2d (0,2) SCFTs, and AdS3xS3/ΓxCY3, dual to 2d (0,4) SCFTs, respectively. In all cases we compute the charges for the fual field theories with varying coupling and find agreement with the holographic results. We also show that solutions with enhanced 2d N=(2,2) supersymmetry must have constant axio-dilaton. Allowing the internal geometry to be non-compact leads to the most general class of Type IIB AdS5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N=1 SCFTs.