Breakthroughs in sequencing technologies led to an exponential growth of genomic data, providing unprecedented biological insights and new therapeutic applications. However, analyzing such large amounts of sensitive data raises key concerns regarding data privacy, specifically when the information is outsourced to third-party infrastructures for data storage and processing (e.g., cloud computing). Current solutions for data privacy protection resort to centralized designs or cryptographic primitives that impose considerable computational overheads, limiting their applicability to large-scale genomic analysis. We introduce GYOSA, a secure and privacy-preserving distributed genomic analysis solution. Unlike in previous work, GYOSA follows a distributed processing design that enables handling larger amounts of genomic data in a scalable and efficient fashion. Further, by leveraging trusted execution environments (TEEs), namely Intel SGX, GYOSA allows users to confidentially delegate their GWAS analysis to untrusted third-party infrastructures. To overcome the memory limitations of SGX, we implement a computation partitioning scheme within GYOSA. This scheme reduces the number of operations done inside the TEEs while safeguarding the users' genomic data privacy. By integrating this security scheme in Glow, GYOSA provides a secure and distributed environment that facilitates diverse GWAS studies. The experimental evaluation validates the applicability and scalability of GYOSA, reinforcing its ability to provide enhanced security guarantees. Further, the results show that, by distributing GWASes computations, one can achieve a practical and usable privacy-preserving solution.