  We discuss the quantization in the minisuperspace for the generalized
fourth-order teleparallel cosmological theory known as $f\left( T,B\right) $.
Specifically we focus on the case where the theory is linear on the torsion
scalar, in that consideration we are able to write the cosmological field
equations with the use of a scalar field different from the scalar tensor
theories, but with the same dynamical constraints as that of scalar tensor
theories. We use the minisuperspace description to write for the first time the
Wheeler-DeWitt equation. With the use of the theory of similarity
transformations we are able to find exact solutions for the Wheeler-DeWitt
equations as also to investigate the classical and semiclassical limit in the
de Broglie -Bohm representation of quantum mechanics.
