Along with half-centuries from Lokesh Rahul (64 from 127 balls; 9x4, 1x6) and skipper Virat Kohli (51 from 94 balls; 4x4), the visitors ended their first innings on 364 all out from 105.4 overs.
Jadeja, who had returned with impressive figures of 3/16 while bowling on the opening day, hit a superb 61-ball 56 down the order with the help of eight boundaries.
At stumps, the hosts were placed at 26 for 1 from eight overs with off-spinner R Ashwin having got the scalp of opening batsman and captain Leon Johnson (17).
After lunch, Rahul did not come out to bat and it was Ajinkya Rahane (32 from 77 balls; 5x4) who accompanied Kohli to the crease.
The Indian skipper reached his fifty in no time, but just as he was looking to get some more time under his belt, he was trapped LBW by Rahkeem Cornwall (5/118).
Rahane then added 44 runs with Stuart Binny (16), before the latter was caught behind off the same bowler.
He had bowled Cheteshwar Pujara (28) in the final over of day one, and after scalping both Kohli and Binny, he then dismissed Rahane as well.
Rahane was looking well set until then, playing some choice strokes, but a sharp turner ballooned to leg slip as he prodded forward.
(REOPENS FGN18)
After tea, Jadeja withstood the new ball taken by the hosts and put on 47 runs along with R Ashwin (26).
It could have been a six-for, but Amit Mishra (10 not out) was put down in the deep off the very first ball.
Mishra then added 19 runs with Ashwin, before the latter was run-out, bringing an end to the Indian innings.
When WICB President's XI batsmen took guard for the second time, Ashwin shared the new ball with Mohammed Shami (0/12) and the duo bowled eight overs.
It looked as if the WICB President XI openers would see through the day, but Ashwin (1/14) dismissed skipper Leon Johnson (17), inducing a delightful return catch.
Rahul batted slowly, looking to run hard, as the slow outfield did not carry the ball to the ropes on a number of occasions.
At the other end, Kohli opened and brought out a flurry of on-drives against the pacers.
Rahul was dropped by Keon Joseph (0/40) when on 49, a simple return catch spilled as the bowler did not get down on time.
The Indian youngster then reached his half-century with a dab to third man, making a strong case for inclusion for the first Test in Antigua.
The WICB President XI side were unlucky not to snare one of the two, as on the last ball before lunch, Rahul edged behind off Joseph again only for stand-in keeper Shai Hope to drop the chance.
It was the third let-off for the young opener in the morning session, after two moments of miscommunication where he could have been run-out.
Brief Scores:
WICB President's XI: 180 all out and 26 for 1 in 8 overs.
India: 364 all out in 105.4 overs (Lokesh Rahul 64, Virat Kohli 51, Ravindra Jadeja 56; Rahkeem Cornwall 5/118).
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