Smart city digital twins can provide useful insights by making effective use of multidisciplinary urban data from diverse sources. Whilst these insights provide new information that helps cities in decision making, verifying the authenticity, integrity, traceability and data ownership across various functional units have become critical characteristics to ensure the data is from an authentic and trustworthy source. However, these characteristics are rarely considered in a digital twin ecosystem. In this research we introduce a novel framework, namely, 'SIGNED: Smart cIty diGital twiN vErifiable Data framework' that is designed on the basis of data ownership, selective disclosure and verifiability principles. Using Verifiable Credentials, SIGNED ensures digital twin data are verifiably authentic i.e., it covers provenance, transparency, and reliability through verifiable presentation. A proof of concept is designed and evaluated based on a smart water management use case to demonstrate the effectiveness of SIGNED in securing verifiable exchange of digital twin data across multiple functional units. The proof-of-concept demonstrates that SIGNED successfully allows the exchange of data in a trusted and verifiable manner at negligible performance cost, thus enhancing security and alleviating privacy issues when sharing data between various functional units in a smart city.