The selectors did not make any changes to the ODI squad apart from adding Patel and retained pacer Ishant Sharma, who was brought in to replace the injured Mohit Sharma.
India and the West Indies are currently locked 1-1 in the ODIs after the third match in Visakhapatnam was cancelled due to cyclone 'hudhud'.
In the Twenty20 side, the selectors rewarded Manish Pandey for his decent performance in the IPL, in which he scored 401 runs in 16 matches this season at an average of 30.84 for Kolkata Knight Riders. His strike rate was an impressive 117.94 during the IPL.
Patel, on the other hand, was in good form with the ball while turning up for Kings XI Punjab this season. He took 17 wickets in 17 games at a fine average of 23.82.
Pandey and Patel replaced Dhawal Kulkarni and Ambati Rayudu in the Twenty20 side, which was last seen in action during the tour of England.
The Twenty20 match between the two sides is scheduled on October 22 in Cuttack.
India ODI squad: Mahendra Singh Dhoni (capt), Shikhar Dhawan, Ajinkya Rahane, Virat Kohli, Suresh Raina, Ambati Rayudu, Ravindra Jadeja, Amit Mishra, Bhuvneshwar Kumar, Mohammed Shami, Ishant Sharma, Umesh Yadav, M Vijay, Kuldeep Yadav, Akshar Patel.
India Twenty20 squad: Mahendra Singh Dhoni (capt), Shikhar Dhawan, Ajinkya Rahane, Virat Kohli, Suresh Raina, Stuart Binny, Ravindra Jadeja, Akshar Patel, Karn Sharma, Bhuvneshwar Kumar, Mohammed Shami, Sanju Samson, Manish Pandey, Umesh Yadav.