Financial exclusion remains one of the most persistent development challenges in Sub-Saharan Africa. According to the World Bank Global Findex Database, account ownership in the region rose from 34% of adults in 2014 to 58% by 2024, yet an estimated 42% of adults still lack access to any formal financial account. A primary structural barrier is the absence of verifiable identity documentation: in many countries, over 40% of unbanked adults cite lack of documentation as a key reason they cannot open an account. Existing digital identity solutions either centralise sensitive personal data on operator servers, creating systemic privacy and security risks, or presuppose smartphone ownership and broadband connectivity that large segments of the population do not yet have. This paper proposes ZKP-IDFS (Zero-Knowledge Proof Identity for Financial Services), a novel privacy-preserving digital identity framework that enables individuals to prove identityrelated predicates to financial institutions without disclosing the underlying personal attributes. The framework integrates Groth16 zk-SNARKs for succinct on-chain proof verification, Pedersen vector commitments for attribute hiding, a W3C Decentralised Identifier and Verifiable Credential layer for interoperability, and an original USSD/SMS proof-relay channel that brings ZKP-based verification to feature-phone users on 2G networks without local proof generation. We formalise the cryptographic model, specify a five-layer system architecture, design the Circom arithmetic circuit encoding the identity predicate relation, and present a controlled simulation-based performance evaluation across three hardware profiles and four network conditions. Simulation results show end-to-end verification completing in under 4.2 seconds on 3G for budget Android devices and under 14.3 seconds via the USSD relay on 2G. On-chain verification on Polygon zkEVM costs below $0.001 per proof. We map the framework against FATF Risk-Based Approach guidance and four African national dataprotection laws, demonstrating that privacy-by-design KYC compliance is achievable within the current regulatory environment. All performance results are simulation-derived and require field validation prior to production deployment.