* HK->Shanghai Connect daily quota used 3.6%, Shanghai->HK daily quota used 1.4%

* HSI -0.4%, HSCE -1.2%, CSI300 +1.1%

* China steps up supervision of overseas-listed firms

SHANGHAI, July 7 (Reuters) - Hong Kong shares ended lower for the seventh straight session on Wednesday to their lowest close in nearly two months, as internet firms led losses after Beijing stepped up supervision of overseas-listed companies on data security. ** At the close of trade, the Hang Seng index was down 112.24 points, or 0.4%, at 27,960.62, the lowest close since May 14. The Hang Seng China Enterprises index fell 1.17% to 10,149.84. ** The sub-index of the Hang Seng tracking energy shares dipped 1.5%, while the IT sector fell 1.56%. The financial sector ended 0.8% lower and the property sector slipped 0.23%.

** Short video streamers Kuaishou Technology fell 3.39% and Bilibili lost 5.05%. Shares of Baidu and Alibaba in Hong Kong fell 2.15% and 1.72%, respectively.

** China will step up supervision of Chinese firms listed offshore, days after Beijing launched a cybersecurity investigation into ride-hailing giant Didi Global Inc on the heels of its U.S. stock market listing.

** Under the new measures, China will improve regulation of cross-border data flows and security, its cabinet said on Tuesday.

** The weakness also echoed to the global markets as investors are nervous about riskier assets before the release of minutes from the Federal Reserve's latest meeting to see if they confirm a hawkish turn in U.S. monetary policy. ** China's main Shanghai Composite index closed up 0.66% at 3,553.72 points, while the blue-chip CSI300 index ended up 1.13%. ** Around the region, MSCI's Asia ex-Japan stock index was weaker by 0.18%, while Japan's Nikkei index closed down 0.96%. ** The yuan was quoted at 6.4652 per U.S. dollar at 08:21, 0.21% firmer than the previous close of 6.4788. (Reporting by the Shanghai Newsroom; Editing by Shailesh Kuber)