In this work, we will consider the singular
Hahn--Sturm--Liouville difference equation defined by
$-q^{-1}D_{-\omega q^{-1},q^{-1}}D_{\omega ,q}y( x) +v(x) y( x)
=\lambda y(x)$, $x\in (\omega _{0},\infty),$ where $\lambda$ is a
complex parameter, $v$ is a real-valued continuous function at
$\omega _{0}$ defined on $[\omega _{0},\infty)$. These type
equations are obtained when the ordinary derivative in the classical
Sturm--Liouville problem is replaced by the $\omega,q$-Hahn
difference operator $D_{\omega,q}$. We develop the $\omega,q$-analogue of the classical
Titchmarsh--Weyl theory for such equations. In other words, we study the existence of
square-integrable solutions of the singular Hahn--Sturm--Liouville
equation. Accordingly, first we define an appropriate Hilbert
space in terms of Jackson--N\"{o}rlund integral and then we study
families of regular Hahn--Sturm--Liouville problems on
$[\omega_{0},q^{-n}]$, $n\in \mathbb{N}$. Then we define a family of
circles that converge either to a point or a circle. Thus, we will
define the limit-point, limit-circle cases in the Hahn calculus
setting by using Titchmarsh's technique.