  Deformed sine-Gordon (DSG) models $\partial_\xi \partial_\eta \, w +
\frac{d}{dw}V(w) = 0$, with $V(w)$ being the deformed potential, are considered
in the context of the Riccati-type pseudopotential approach. A compatibility
condition of the deformed system of Riccati-type equations reproduces the
equation of motion of the DSG models. Then, we provide a pair of linear systems
of equations for DSG model, and provide an infinite tower of non-local
conservation laws. Through a direct construction and supported by numerical
simulations of soliton scatterings, we show that the DSG models, which have
recently been defined as quasi-integrable in the anomalous zero-curvature
approach [Ferreira-Zakrzewski, JHEP05(2011)130], possess new towers of infinite
number of quasi-conservation laws. We compute numerically the first sets of
non-trivial and independent charges (beyond energy and momentum) of the DSG
model: the two third order conserved charges and the two fifth order
asymptotically conserved charges in the pseudopotential approach, and the first
four anomalies of the new towers of charges, respectively. We consider
kink-kink, kink-antikink and breather configurations for the Bazeia {\sl et
al.} potential $V_{q}(w) = \frac{64}{q^2} \tan^2{\frac{w}{2}}
(1-|\sin{\frac{w}{2}}|^q)^2 \, (q \in R)$, which contains the usual SG
potential $V_2(w) = 2[1- \cos{(2 w)}]$. The numerical simulations are performed
using the 4th order Runge-Kutta method supplied with non-reflecting boundary
conditions.
