In recent times, fog computing has emerged as a helpful extension of cloud computing. It can efficiently handle the prevalent issue of managing silos of data generated by today's digital healthcare services. Moreover, the application of the Internet of Things (IoT) in the development of smart healthcare systems further adds tons of data tirelessly to these silos, thus making the cloud congested. To manage such continuously growing data, the concept of adding a fog layer between the cloud and the end-users (EUs) proved to be beneficial. These intermediary fog nodes (FNs) can handle and store data, and thus facilitate the cloud and alleviate the burden from the EUs. Most of the existing search schemes for encrypted data have been developed for the cloud platform and ignored this helpful extension, which can improve the scheme's efficiency by delegating most of the heavy computations to the intermediary FNs. In this article, a fine-grained searchable data sharing scheme has been proposed using the fog computing platform. The resulting scheme is efficient and lightweight because the FN facilitates EUs by performing computationally intensive tasks on their behalf. A significant reduction in storage and computational cost has been achieved by the proposed scheme at the data owner's end, representing the resource-constrained IoT devices. The storage cost has been reduced to two source group elements, and the computational cost has been reduced to three exponent operations in the source group and one hash operation. Furthermore, the proposed scheme is secure against the selectively chosen keyword attack in the generic bilinear group model.