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We have prepared and investigated superconducting equimolar medium-entropy alloys of TiZrNb and TiZrNbHf. Their basic superconducting parameters, as the values of the critical temperature T_c, upper critical magnetic field B_c2 and the superconducting energy gap Δ have been studied with the use of magnetic susceptibility and point-contact Andreev reflection (PCAR) spectroscopy measurements. Although our samples have different critical temperatures, namely T_c ∼ 8.2 K for TiZrNb and T_c ∼ 6.3 K for TiZrNbHf, their zero-temperature critical magnetic field has the same value B_c2(0) = 12 T, from the vicinity of the Clogston limit. We have observed the presence of degraded phases on the surfaces of all the investigated samples using PCAR measurements. Still, we were able to show that the bulk phase in both systems exhibits BCS weakly coupled superconductivity with 2Δ(0)/k_BT_c ∼ 3.5.