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Abstract The Josephson effect in point contacts between an “ordinary” superconductor $$\hbox {Pb}_{0.6}$$ Pb 0.6 In $$_{0.4}$$ 0.4 ( $$T_c \approx 6.6 \, {\mathrm {K}}$$ T c ≈ 6.6 K ) and single crystals of the Fe-based superconductor Ba $$_{0.6}$$ 0.6 K $$_{0.4}$$ 0.4 (FeAs) $$_2$$ 2 ( $$T_c \approx 38.5 \, {\mathrm {K}}$$ T c ≈ 38.5 K ), was investigated. In order to shed light on the order parameter symmetry of Ba $$_{0.6}$$ 0.6 K $$_{0.4}$$ 0.4 (FeAs) $$_2$$ 2 , the dependence of the Josephson supercurrent $$I_s$$ I s on the temperature and on $$\sin (d\varphi )$$ sin ( d φ ) with $$d = 1, 2$$ d = 1 , 2 was studied. The dependencies of the critical current on temperature $$I_c (T)$$ I c ( T ) and of the amplitudes of the first current steps of the current–voltage characteristic $$i_n^{exp} (\sqrt{P})$$ i n exp ( P ) $$(n = 0, 1, 2)$$ ( n = 0 , 1 , 2 ) on the power of microwave radiation with frequency $$f = (1.5 \div 8)\, {\mathrm {GHz}}$$ f = ( 1.5 ÷ 8 ) GHz were measured. It is shown that the dependencies $$I_c (T)$$ I c ( T ) are close to the well-known Ambegaokar–Baratoff (AB) dependence for tunnel contacts between “ordinary” superconductors and to the dependence calculated by Burmistrova et al. (Phys Rev B 91, 214501 (2015)) for microshorts between an “ordinary” superconductor and a two-band superconductor with $$s \pm$$ s ± order parameter symmetry at certain values of the transparency of boundaries and thickness of the transition layer. It is found that the dependencies $$i_n^{exp} (\sqrt{P})$$ i n exp ( P ) cannot be approximated within the resistively shunted model using the normalized microwave frequencies $$\Omega = 2 \pi f / (2eV_c / \hbar )$$ Ω = 2 π f / ( 2 e V c / ħ ) with characteristic voltages $$V_c = I_c R_N$$ V c = I c R N , $$(R_N$$ ( R N —normal resistance of the contact) found from the low-voltage parts of the current–voltage characteristics. The reasons for this failure are discussed and a method is proposed for accurately determining the value of $$\Omega$$ Ω , which takes into account all the features of the point contact affecting the period of the dependence $$i_n^{exp} (\sqrt{P})$$ i n exp ( P ) . An analysis of the $$I_c (T)$$ I c ( T ) and $$i_n^{exp} (\sqrt{P})$$ i n exp ( P ) dependencies shows that the superconducting current of the Josephson contacts under investigation is proportional to the $$\sin$$ sin of the phase difference $$\varphi$$ φ , $$I_s = I_c sin(\varphi )$$ I s = I c s i n ( φ ) . The implications of these results on the symmetry of the order parameter are also discussed.