  We study the constructible Witt theory of \'etale sheaves of
$\Lambda$-modules on a scheme $X$ for coefficient rings $\Lambda$ having finite
characteristic not equal to 2 and prime to the residue characteristics of the
scheme $X$. Our construction is based on the recent advances by Cisinski and
Deglise on six-functor formalism for derived categories of \'etale motives and
offers a background for the of study of constructible Witt theory as a
cohomological invariant for schemes.
