<p>Verifiably encrypted signature (VES) schemes are extensively utilized in fair exchange which combine the features of encryption and signature, aiming to provide a solution that can not only verify the validity of signatures but also safeguard the privacy of signatures. With the development of quantum algorithms and quantum computing, it is necessary to construct a VES protocol that can resist attack of quantum computing. At the same time, some new security properties can also be added to the VES protocol to enhance its security. To reach this goal, we propose a state-of-the-art lattice-based verifiably encrypted group signature (VEGS) scheme. In the random oracle model, the VEGS scheme is provably secure under the assumptions of learning with error (LWE) and inhomogeneous small integer solution (ISIS). Our scheme provides five security properties, namely unforgeability, opacity, extractability, anonymity and traceability. The three properties unforgeability, opacity and extractability are the properties that the VES protocol needs to meet, and the anonymity and traceability properties are additional security properties brought by combining with the group signature.</p>