  In this paper, we will try to present a general formalism for the
construction of {\it deformed photon-added nonlinear coherent states} (DPANCSs)
$|\alpha, f, m>$, which in special case lead to the well-known photon-added
coherent state (PACS) $|\alpha, m>$. Some algebraic structures of the
introduced DPANCSs are studied and particularly the resolution of the identity,
as the most important property of generalized coherent states, is investigated.
Meanwhile, it will be demonstrated that, the introduced states can also be
classified in the $f$-deformed coherent states, with a special nonlinearity
function. Next, we will show that, these states can be produced through a
simple theoretical scheme. A discussion on the DPANCSs with negative values of
$m$, i.e., $|\alpha, f, -m>$, is then presented. Our approach, has the
potentiality to be used for the construction of a variety of new classes of
DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity
function, as well as arbitrary solvable quantum system with known discrete,
nondegenerate spectrum. Finally, after applying the formalism to a particular
physical system known as P\"oschl-Teller (P-T) potential and the nonlinear
coherent states corresponding to a specific nonlinearity function $f(n)=\sqrt
n$, some of the nonclassical properties such as Mandel parameter, second order
correlation function, in addition to first and second-order squeezing of the
corresponding states will be investigated, numerically.
