  We construct and thoroughly study a new integrable example of the AdS/CFT
correspondence with Schr\"{o}dinger symmetry. On the gravity side, the
supergravity solution depends on two parameters and is obtained by marginally
deforming the internal space of the Schr\"{o}dinger background through a series
of TsT transformations. On the field theory side, we identify the dual field
theory which also depends on two parameters. We find a point-like string
solution and derive its dispersion relation. A non-trivial test of the
correspondence is provided by using the Landau-Lifshitz coherent state approach
to reproduce the leading, in the deformation parameters, terms of that
relation. Then, we calculate the Wilson loop, describing the quark/anti-quark
potential at strong coupling. It exhibits confining behaviour when the
separation length is much less than the Schr\"{o}dinger parameter. When the
separation length is much greater than the Schr\"{o}dinger parameter the
behaviour is that of a conformal theory. Subsequently, we take the Penrose
limit along a certain null geodesic of the constructed background and calculate
the bosonic spectrum. Based on that spectrum, we make an educated guess for the
exact, in the 't Hooft coupling, dispersion relation of the magnon excitations
in the original doubly deformed background. This provides us with an exact
prediction for the dimensions of the dual field theory operators.
