Fingering convection in a horizontal doubly stratified fluid-saturated porous medium is examined under the influence of modulating gravitational field. The Brinkman model of momentum transfer is considered, and the Boussinesq approximation is assumed for natural convection. Floquet theory is employed to determine the onset condition within the framework of linear theory. Continued fractions that can handle arbitrary modulational parameters has been used to predict the dynamic instability regions at the marginal state and critical instability boundaries. Certain combinations of solutal Rayleigh and Schmidt numbers give rise to the occurrence of doubly unstable regions. An increase in the modulation amplitude always encourages instability. The competition between synchronous and subharmonic instability modes is observed for a certain range of values of the parameters. Solutal convection is found to introduce closed disconnected instability loops at the marginal state. It is seen that gravity modulation effects disappear for higher modulational frequencies. The results could be of use in applications like enhanced oil recovery from geothermal reservoirs and solidification of binary alloys, among others.