  Given a topologically transitive subshift of finite type, the $u$-dimension
of the $\alpha$-level set of the quotient of Birkhoff sums is a well-studied
topic. In this paper, we consider the uniform $\alpha$-level set, which is a
subset of the $\alpha$-level set. We shall show that the $\alpha$-level set and
the uniform $\alpha$-level set have the same $u$-dimension. Moreover, we also
consider two types of subsets of the $\alpha$-level set, whose elements are
sequences satisfying some constraints on their subwords. We shall show that for
$\alpha$ not on the boundary of the dimension spectrum, these subsets also have
the same $u$-dimension as the $\alpha$-level set. As an application, we shall
perform a multifractal analysis of the Hoelder regularity of a Gibbs measure on
a one-dimensional manifold.
