On ternary Diophantine equations of signature (p, p, 2) over number fields

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.