HONG KONG, Jan 3 (Reuters) - China shares wobbled, and Hong Kong stocks extended declines on Wednesday, tracking a broader Asian sell-off, while investors remained cautious due to the uncertainty about the economic recovery.

** The blue-chip CSI 300 Index slid 0.2%, while the Shanghai Composite Index edged up 0.2%.

** Hong Kong's Hang Seng Index dropped 0.9% and the Hang Seng China Enterprises Index fell 0.8%.

** "The sluggishness in economic recovery and policy uncertainty is keeping investors cautious," said Redmond Wong, Greater China market strategist at Saxo Markets.

** The correction overnight in the U.S. also weighed on regional markets, he added.

** Broader Asian shares extended a global sell-off, as market optimism about early and aggressive U.S. interest rate cuts waned ahead of the release of the Federal Reserve's last monetary policy meeting minutes and jobs data.

** Some of China's top banks have sharpened scrutiny of smaller peers' asset quality and tightened standards for interbank lending, in an effort to curb credit risk as a deepening property debt crisis ripples through the economy, Reuters reported on Wednesday.

** Putting together December Caixin and official PMI reflect further softness in domestic demand conditions and slowing service sector, with manufacturers focussing on export market competition, J.P. Morgan analysts said in a note.

** Artificial intelligence-related stocks dropped 2.8% and information technology companies fell 2.2% to lead the decline.

** Chinese gaming stocks rose 1%, outperforming a weak broader market, following Reuters' report on the removal of a gaming regulatory official in China, seen as a step to calm the market.

** But Saxo Markets' Wong said this move, coupled with the People's Bank of China's injection of funds, is insufficient to impact the big picture.

** "The Hong Kong and mainland A-share markets are still in the process of finding a bottom," he said.

** Hong Kong-listed tech giants dropped 1.8%. (Reporting by Summer Zhen; Editing by Rashmi Aich and Dhanya Ann Thoppil)