* HK->Shanghai Connect daily quota used 3.4%, Shanghai->HK daily quota used 3.1% * FTSE China A50 -0.4% BEIJING/SHANGHAI, Dec 29 (Reuters) - China stocks dropped on Tuesday, dragged down by material and energy shares, as investors booked profit following the recent rally fuelled by continued policy support and upbeat data underscoring economic recovery. ** At the midday break, the Shanghai Composite index was down 0.33% at 3,386.14 points, while the blue-chip CSI300 index was down 0.26%. ** Several sub-indexes recorded losses by the mid-day break, with the material sub-index dropping 1.9%, the energy sub-index falling 1.54% and the consumer staples sector slipping 1.25%. ** The smaller Shenzhen index was down 0.43%, the start-up board ChiNext Composite index was weaker by 0.77%, while Shanghai’s tech-focused STAR50 index was up 0.12%. ** The recent rally offered an opportunity for investors to take profits before the year-end, but continued policy support expressed in the latest economic working conference, and signs of economic recovery will back the performance in a long run, said Zhang Qi, an analyst with Haitong Securities. ** China’s factory activity likely maintained a solid pace of expansion in December, a Reuters poll showed on Tuesday, as the world’s second-largest economy steadily recovers from the coronavirus crisis. ** China is scheduled to release its official manufacturing Purchasing Manager’s Index (PMI) on Thursday. ** Chinese H-shares listed in Hong Kong rose 1.45% to 10,460.52, while the Hang Seng Index was up 1.05% at 26,590.62. ** Around the region, MSCI’s Asia ex-Japan stock index was weaker by 0.18%, while Japan’s Nikkei index was up 1.52%. ** The yuan was quoted at 6.533 per U.S. dollar, 0.08% firmer than the previous close of 6.5383.