  The notion of a $(\varphi,\hat{G})$-module is defined by Tong Liu in 2010 to
classify lattices in semi-stable representations. In this paper, we study
torsion $(\varphi,\hat{G})$-modules, and torsion p-adic representations
associated with them, including the case where p=2. First we prove that the
category of torsion p-adic representations arising from torsion
$(\varphi,\hat{G})$-modules is an abelian category. Secondly, we construct a
maximal (minimal) theory for $(\varphi,\hat{G})$-modules by using the theory of
\'etale $(\varphi, \hat{G})$-modules, essentially proved by Xavier Caruso,
which is an analogue of Fontaine's theory of \'etale
$(\varphi,\Gamma)$-modules. Non-isomorphic two maximal (minimal) objects give
non-isomorphic two torsion p-adic representations.
