  We construct counterexamples for the fractal Schr\"odinger convergence
problem by combining a fractal extension of Bourgain's counterexample and the
intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same
regularity as Du's counterexamples for weighted $L^2$ restriction estimates is
achieved for the convergence problem. To do so, we need to construct the set of
divergence explicitly and compute its Hausdorff dimension, for which we use the
Mass Transference Principle, a technique originated from Diophantine
approximation.
