Let K be a totally real number field with narrow class number one and O K be its ring of integers. We prove that there is a constant B K depending only on K such that for any prime exponent p > B K the Fermat type equation x p + y p = z 2 with x, y, z ∈ O K does not have certain type of solutions. Our main tools in the proof are modularity, level lowering and image of inertia comparisons.