(Refiles to correct dateline) * SSEC -0.1%, CSI300 -0.1%, HSI 0.4% * HK->Shanghai Connect daily quota used -2%, Shanghai->HK daily quota used 3.7% * FTSE China A50 -0.1% SHANGHAI, June 1 (Reuters) - China stocks fell as Tuesday, as losses in financials and new energy firms outweighed gains in birth and fertility related companies on policy cheer. ** The CSI300 index fell 0.1% to 5,325.28 at the end of the morning session, while the Shanghai Composite Index lost 0.1% to 3,611.33. ** Falling most, the CSI300 financials index and the CSI new energy index skid 1.2% and 1.1%, respectively, as investors booked profits following recent strong gains. ** China Industrial Securities Co Ltd and Shanghai Putailai New Energy Technology Co Ltd dropped 5.3% and 5.2%, respectively, ** In May, the financials index was up 5%, while the new energy index climbed 10.6%. ** Bucking the broad weakness, birth and fertility related companies extended gains on Tuesday, as investors continued to cheer Beijing’s major policy support. ** Married Chinese couples may have up to three children, China announced on Monday, in a major shift from the existing limit of two after recent data showed a dramatic decline in births in the world’s most populous country. ** Hubei Goto Biopharm Co Ltd, Jiangsu Aoyang Health Industry Co Ltd, Shanghai Aiyingshi , Beingmate Co Ltd and Goldlok Holdings Guangdong Co Ltd climbed between 5% and 10%. ** But analysts and traders expected limited impact from the policy shift on the market as a whole. ** “The three-child policy could have an impact on China’s long-term economic growth, while its stimulus could be limited for those who already have two children,” said Luo Kun, an investment manager at Chasing Securities’ equities investment arm. ** Luo said he did not see a major impact on the stock market, noting gains for related companies could mainly be a result of short-term speculation. ** The Hang Seng index added 0.4% to 29,275.77, while the Hong Kong China Enterprises Index gained 0.4%, to 10,933.23. (Reporting by Luoyan Liu and Andrew Galbraith; Editing by Rashmi Aich) Our Standards: The Thomson Reuters Trust Principles.