Public key encryption with keyword search (PEKS) allows users to perform keyword searches of ciphertext on untrusted cloud storage servers, protecting data privacy while sharing data. However, it faces several security problems in practical applications. First, an attacker can launch a keyword guessing attack to obtain keywords of interest to users, causing the leakage of their sensitive information. Second, untrusted cloud servers may return incorrect or incomplete results. In addition, with the continuous development of quantum computers, existing PEKS schemes face the problem of quantum attacks. Since cloud servers are mostly untrusted, verifiable search has become a hot research topic among scholars. However, most of the current schemes are based on bilinear pairing constructions, which are vulnerable to quantum attacks. To solve these problems, we propose a new ciphertext retrieval scheme based on fully homomorphic encryption (FHE), called VR-PEKS. This scheme implements verifiable search and is able to solve the problems of keyword guessing attacks and quantum attacks. We propose to improve the security of the scheme by using the oblivious pseudorandom function to randomize keywords and then encrypt them using FHE. An encrypted verified index structure is constructed and exposed by the data owner, enabling the data recipient to achieve verification of the correctness and integrity of the retrieved results without relying on a trusted third party. We demonstrate the security of the proposed scheme in a stochastic prediction model, and prove that our scheme satisfies keyword ciphertext indistinguishability and keyword trapdoor indistinguishability under adaptive keyword selection attacks. The comparison shows that our scheme is secure and feasible.