Using the effective mass approximation and a variational procedure, we have calculated the effects of confining potential and growth-direction applied magnetic field on the binding energy and photoionization cross section of a donor impurity in a cylindrical InAs Pöschl-Teller quantum layer. We report the binding energy dependencies on the height and the inner and outer radii of the cylindrical layer, the applied magnetic field, and the parameters of the Pöschl-Teller confining potential. The dependencies of the impurity-related photoionization cross section on the incident photon energy for the different values of the confining potential parameters and the geometrical parameters of the heterostructure have been also considered. The results show that the impurity related binding and energy photoionization cross section are non monotonic functions of the inputs here considered. Particularly, it is shown that the binding energy increases with the increase inner radius of the layer and decrease with the all another inputs considered in this work (height and outer radius of the layer, applied magnetic field, and asymmetry of the Pöschl-Teller potential). In the case of the photoionization cross section the results show that with changes in the dimensions of the heterostructure and in the symmetry of the potential both blue shift and/or red shift of the maximum of the lineshape can be induced.