When a second-order magnetic phase transition is tuned to zero temperature by a nonthermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these "quantum critical" superconductors it has been widely reported that the normal-state properties above the superconducting transition temperature T c often exhibit anomalous non-Fermi liquid behaviors and enhanced electron correlations. However, the effect of these strong critical fluctuations on the superconducting condensate below T c is less well established. Here we report measurements of the magnetic penetration depth in heavy-fermion, iron-pnictide, and organic superconductors located close to antiferromagnetic quantum critical points, showing that the superfluid density in these nodal superconductors universally exhibits, unlike the expected T-linear dependence, an anomalous 3/2 power-law temperature dependence over a wide temperature range. We propose that this noninteger power law can be explained if a strong renormalization of effective Fermi velocity due to quantum fluctuations occurs only for momenta k close to the nodes in the superconducting energy gap Δ(k). We suggest that such "nodal criticality" may have an impact on low-energy properties of quantum critical superconductors. T he physics of materials located close to a quantum critical point (QCP) are an important issue because the critical fluctuations associated with this point may produce unconventional high-temperature superconductivity (1, 2). Quantum oscillations (3, 4) and specific heat measurements (5) have shown that, in some systems, as the material is tuned toward the QCP by controlling an external parameter such as doping, pressure, or magnetic field, the effective mass strongly increases due to enhanced correlation effects. Along with this the temperature dependence of the resistivity shows a strong deviation from the standard AT 2 dependence in the Fermi liquid (FL) theory of metals and often shows an anomalous T-linear behavior that corresponds to the A coefficient diverging as zero temperature is approached.Although there are many studies of non-FL behavior in the normal metallic state (1, 2), relatively little is known about how the QCP affects the superconducting properties below the critical temperature T c . The superconducting dome often develops around the putative QCP so that when the temperature is lowered below T c , the superconducting order parameter starts to develop and the Fermi surface becomes gapped. It is therefore natural to consider that the low-energy quantum critical fluctuations are quenched by the formation of the superconducting gap Δ, which means that the system avoids the anomalous singularities associated with the QCP. Perhaps because of this reasoning the superconducting properties are usually analyzed by the conventional theory without including temperature/field-dependent renormalization effects resulting from the proximity to the QCP. For example, in refs. 6 and 7 the NMR relaxat...