Traditional database fuzzing techniques primarily focus on syntactic correctness and general SQL structures, leaving critical yet obscure DBMS features, such as system-level modes (e.g., GTID), programmatic constructs (e.g., PROCEDURE), advanced process commands (e.g., KILL), largely underexplored. Although rarely triggered by typical inputs, these features can lead to severe crashes or security issues when executed under edge-case conditions. In this paper, we present FuzzySQL, a novel LLM-powered adaptive fuzzing framework designed to uncover subtle vulnerabilities in DBMS special features. FuzzySQL combines grammar-guided SQL generation with logic-shifting progressive mutation, a novel technique that explores alternative control paths by negating conditions and restructuring execution logic, synthesizing structurally and semantically diverse test cases. To further ensure deeper execution coverage of the back end, FuzzySQL employs a hybrid error repair pipeline that unifies rule-based patching with LLM-driven semantic repair, enabling automatic correction of syntactic and context-sensitive failures. We evaluate FuzzySQL across multiple DBMSs, including MySQL, MariaDB, SQLite, PostgreSQL and Clickhouse, uncovering 64 vulnerabilities, 27 of which are tied to under-tested DBMS special features. As of this writing, 60 cases have been confirmed with 9 assigned CVE identifiers, 31 already fixed by vendors, and additional vulnerabilities scheduled to be patched in upcoming releases. Our results highlight the limitations of conventional fuzzers in semantic feature coverage and demonstrate the potential of LLM-based fuzzing to discover deeply hidden bugs in complex database systems.