Modified Newtonian Dynamics (MOND) is built on a universal critical acceleration a0, with a long-standing numerical coincidence between the local best-fit a0 and cH0/(2π). Previous tests of a0’s cosmic evolution have been limited by baryonic modeling systematics and the narrow applicability of the deep-MOND approximation. Here we define a dimensionless observable B(z) ≡ a2 tot/(cH(z)aN), which cancels structural systematics and directly probes a0(z)/(cH(z)) in the weak-acceleration regime. Under the hypothesis a0(z) = cH(z)/(2π), B(z) is predicted to be a universal constant 1/(2π) ≈ 0.159. We test this prediction with three complementary datasets: 175 nearby SPARC galaxies, 1207 radial acceleration points from the SPARC sample in the strict deep-MOND regime (atot < 0.1a0), and 5 high-redshift regular rotating disk galaxies (z = 0.56 − 2.10) from the ALMA ALPAKA survey. We find the deep-MOND local sample yields B = 0.158±0.020, in agreement within uncertainties with the theoretical prediction. For high-redshift galaxies in the strong-acceleration regime, we apply an analytical correction based on the standard MOND interpolation function, with uncertainties propagated via Monte Carlo error propagation to ensure rigorous error estimation. Corrected values are fully consistent with 1/(2π) within uncertainties. We find no statistically significant evidence for redshift evolution of B(z), with a linear slope of 0.010 ± 0.009 (consistent with zero at 1.1σ).This result is robust to selection criteria and cosmological parameter choices. Our findings serve as a preliminary consistency check for the proposed cosmological scaling of a0. With the current small high-redshift sample, we cannotplace strong constraints on evolution; future high-resolution observations with JWST and ALMA will be needed to test the redshift dependence more robustly.