Abstract
In this paper, a new q-analogue of modified Bessel, function and its corresponding generating function are given. Also, we used the generating function method to deduce its q-difference equation which gives us the differential equation of the ordinary modified Bessel function when q -> 1 and we deduced its recurrence relation. Finally, we established the relation between the two-dimensional quantum algebra E-q(2) and the new q-analogue of modified Bessel function using the realization of the standard Euclidean algebra in one real variable and q-exponentials.