The Global Alliance for Genomics and Health (GA4GH) Beacon protocol lets researchers ask whether a genomic variant has been observed in a participating cohort and receive aggregate variant-level counts. As Beacon networks grow, two privacy risks remain: host institutions can see plaintext queries, and repeated rare-variant queries can support membership-inference attacks. We present bioETH-Beacon, a smart-contract prototype that runs the Beacon "aggregate count" query over encrypted data on a fully homomorphic Ethereum Virtual Machine (fhEVM). Hospitals upload encrypted marker-count entries, authorized researchers submit encrypted marker queries, and the contract returns an encrypted answer that is released, via an off-chain key-management service, only to the requester named in the contract's on-chain ACL. The design is organized as a 3x4 tier-by-query-family grid spanning genotype, sex, age, and phenotype queries, with tiers that trade stronger confidentiality for lower query cost. For genotype paths, the prototype can add bounded on-chain noise to mitigate probing attacks. Experiments on synthetic panels derived from a Polygenic Score (PGS) catalog show the expected scaling behavior and demonstrate that pre-aggregation can substantially reduce query gas when public marker presence is an acceptable trade-off. Overall, bioETH-Beacon provides a research prototype for confidential Beacon-style genomic querying without a trusted compute evaluator.