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An important document for names, authority and distribution of Asteraceae (=Compositae) species in India is FLOWERING PLANTS OF INDIA, DICOTYLEDONS, Vol-I (Acanthaceae-Avicenniaceae) authored by S.Karthikeyan, M.Sanjappa and S.Moorthy.
It is published by Botanical Survey of India, Kolkata in 2009.
As per this document (Karthikeyan et al., 2009) following species of Cissampelopsis occur in India:

1- Cissampelopsis anstaedi,
2- C.buimalia,
3- C.calcadensis,
4- C.corifolia,
5- C.corymbosa,
6- C.vivekananthanii,
7- C.volubilis,
8- C.walkeri.

No Cissampelopsis species seems threatened in India as Red Data Book of Indian Plants (Nayar & Sastry, 1987-90) does not mention any species.
It is interesting to note that the genus Cissampelos [http://www.theplantlist.org/tpl/search?q=Cissampelosis in Menispermaceae family while Cissampelopsis
is in Asteraceae.
 
  


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A revision of Cissampelopsis (Asteraceae: Senecioneae) Kew Bulletin 63:213-226 · January 2008:
Key to the species of Cissampelopsis
1. Capitula radiate; ray and disc corollas truly yellow; style arm penicillate, apices without central tuft of longer papillae (sect. Buimalia)……2
– Capitula discoid; corolla pale yellow or pinkish to white; style arm penicillate, apices with central tuft of longer papillae (sect. Cissampelopsis)….4
2. Capitula with 5 –6 ray florets and about 10 –15 disc florets; phyllaries 8 ……………1. C. buimalia
– Capitula with 8 –13 ray florets and about 20 disc florets; phyllaries 13 …………3
3. Leaf apex apiculate, apex about 2 –3 mm long; pappus reddish . . . . .  . 2. C. erythrochaeta
– Leaf apex acuminate, apex about 5 –10 (20) mm long; pappus yellowish . . . . . . . . .3. C. calcadensis
4. Capitula with 5 –10 disc florets; leaves sparsely arachnoid-tomentose or fulvous-glandular to glabrous beneath…………5
– Capitula with 15 –20 disc florets; leaves denselyand persistentlyarachnoid-tomentose beneath………….9
5. Stem and leaves densely fulvous-glandular; panicle shorter than leaves . ……..4. C. glandulosa
– Stem and leaves sparsely to densely arachnoid-tomentose to floccose or almost glabrous; panicle longer than leaves………6
6. Leaf margin callose-denticulate with minute teeth; phyllaries glabrous or almost so . . ……..7
– Leaf margin sinuate-denticulate with mucronulate teeth; phyllaries sparsely arachnoid-tomentose . . . . . 8
7. Leaf blade papyraceous to herbaceous with shortly apiculate apex about 2 –5 mm long; stem and leaves sparsely arachnoid-tomentose to subglabrous ….5. C. walkeri
– Leaf blade coriaceous with acuminate apex about 5 –10 (20) mm long; stems and leaves glabrous . . . 6. C. corifolia
8. Phyllaries 8; disc florets 8 –10…………….7. C. volubilis
– Phyllaries 5 –6; disc florets 5 –6…………..8. C. ansteadii
9. Capitula about 5 –8 in terminal and axillary panicles; leaf blade papyraceous . . . ………9. C. spelaeicola
– Capitula more than 8 in terminal and axillary panicles; leaf blade coriaceous to subcoriaceous . . . 10. C. corymbosa

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A Revision of Cissampelopsis (Asteraceae: Senecioneae) – jstor (2008)- Details with Keys of all 10 species & 2 varieties.
Species found in India are:

Binomial Habit Notes References Distribution
Cissampelopsis
ansteadii
(Tad. & Jacob) C. Jeffrey & Y.L.
Chen 
Shrubby Climber Western Ghats,
Evergreen  Forests, Endemic
R.Gopalan &
A.N.Henry 2000
Kanniya kumari,
Tirunelveli
Cissampelopsis corymbosa (DC.) C. Jeffrey
& Y. L. Chen
Climber Western
Ghats, Evergreen Forests, Epiphyte
Flora
of Tamil Nadu, VOL. II, 1987
Coimbatore,
Dindigul, Nilgiri, Theni 
Cissampelopsis walkeri  (Arn.) C. Jeffrey & Y. L. Chen Climber Western
Ghats, Evergreen Forests, Epiphyte
Flora
of Tamil Nadu, VOL. II, 1987
Dindigul, Kanniya kumari, Nilgiri
Senecio calcadensis Ramaswami (syn. of Cissampelopsis calcadensis C.Jeffrey & Y.L.Chen ) Shrub Western Ghats,
Evergreen Forests
Flora of Tamil
Nadu, VOL. II, 1987
Tirunelveli,
Virudhu nagar

I have updated eFI (efloraofindia) page on Senecio, Cissampelopsis, Curio, Jacobaea, Kleinia, Ligularia & Synotis     

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. It’s quite possible that there may be some discrepancy in the accepted names & synonyms taken from other links.

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 also added the list of Indian species of Cissampelos and Kleinia as per the reference mentioned.


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Pl. go through Cissampelopsis (‎‎‎‎‎Asteraceae (Compositae)‎) page with images of species (done by me) in efloraofindia.

If you find any mis-identification, pl. let us know. If anybody can send images of other species of this genera (for incorporation in the website), if any, it will be really nice.

Also, if anybody is interested to take up the activity of inserting images on efloraofindia pages from efloraofindia posts, pl. let us know.