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Using a radio frequency tunnel diode oscillator technique, we measured thetemperature dependence of the in-plane London penetration depth$\Delta\lambda_{ab}(T)$ in Fe$_{1+y}$(Te$_{1-x}$Se$_{x})$ single crystals, downto temperatures as low as 50 mK. A significant number of samples, with nominalSe concentration $x$=0.36, 0.40, 0.43 and 0.45 respectively, were studied andin many cases we found that $\Delta\lambda_{ab}(T)$ shows an upturn below 0.7K, indicative of a paramagnetic type contribution. After subtracting themagnetic background, the low temperature behavior of penetration depth is bestdescribed by a power law with exponent $n\approx2$ and with no systematicdependence on the Se concentration. Most importantly, in the limit ofT$\rightarrow$0, in some samples we observed a narrow region of lineartemperature dependence of penetration depth, suggestive of nodes in thesuperconducting gap of Fe$_{1+y}$(Te$_{1-x}$Se$_{x})$.

Possible nodal superconducting gap in Fe$_{1+y}$(Te$_{1-x}$Se$_{x}$) single crystals from ultra-low temperature penetration depth measurements