In Flora of India Vol-3. (Eds.-B.D. Sharma, M. Sanjappa and N.P. Balakrishnan; published by Botanical Survey of India) the account of Indian Theaceae is written by A.S.Chauhan & T.K. Paul.
As per this document Chauhan & Paul (1993) following species of Schima occur in India:
Schima wallichii (DC.) Korthals
            var. khasiana (Dyer) Bloem. [synonym of Schima khasiana Dyer
            var. wallichii

Binomial Habit Notes References Distribution
Schima wallichii (DC.) Korth Large Tree Western Ghats, Cultivated,  Native of Himalaya  Flora of Tamil Nadu, VOL. I, 1983; Matthew, 1969 Dindigul, Nilgiri

The Growth Pattern of Two Species of Schima by Ram Boojh and P. S. Ramakrishnan- BIOTROPICA 15(2): 142-147 1983
ABSTRACT- The growth patterns of two closely related deciduous tree species, Schima wallichii (at 100 m and 1600 in altitude), and S. khasiana (at 1900 m) in Meghalaya, north-eastern India, were compared. Both species conform to Rauh's model of architecture. Sylleptic lateral branches formed on S. khasiana during periods of vigorous growth of the main shoot. Although stem extension and leaf production were continuous throughout the growing season, they exhibited (endogenous') periodicity which was most marked in S. wallichi, at lower altitude. Schima wallichi at lower altitude had the fastest turnover of leaves.
Forest Plants of Eastern India By Amal Bhusan Chaudhuri (1993)- Details- p. 131-
Schima crenata Korth. (No distribution in current India as per Flora of China)
Schima mollis Dyer (Unresolved)
Indigenous Drugs Of India By Chopra R N, I.C. Chopra- Details-
Schima1 post by 1 author.

I have updated eFI (efloraofindia) page on Schima

Attempts have been made to incorporate most of the species available in India & nearby areas with details & keys directly or through links as far as possible.

Species discussed so far in efloraofindia are given at the bottom of the page in the form of links against Subpages. On clicking them one can see all the details.

Any comments/ corrections are welcome.

I have added name of Indian species based on Flora of India vol-3.