This is Marsilea minuta, a common plant of damp fields, rice-fields, and ponds. To confirm the identity you need to show the sorocarps, which are borne on the lower-growing, smaller, non-aquatic plants, But it is no problem as only M. minuta is in northern India, including J. & K..
In the past such plants were often mistaken for the European M. quadrifolia, which is not present in India - but that has a quite different position of the sorocarps - on the lower leaf-petiole, as opposed to in the axil of the petiole and basal stem.
It's also edible.
Chris Fraser-Jenkins.
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With regards,
J. M. Garg