A prototype 'Fulcrum-D' undergoing flight tests from Aircraft Carrier Admiral Kuznetsov during the time of the Soviet Union.
At the end of its production run, the MiG Corporation would have successfully executed its contract to supply the Indian Navy with 45 Carrier-borne variants of the MiG-29 fighter aircraft. Of these, there would be 41 single-seat MiG-29K while the 4 twin-seat MiG-29KUB variant would make up rest of the Navy's inventory. While the first production variant of the aircraft took to air only in March 2008, the history of development of this variant dates much further back into Soviet Russia. With the collapse of the Soviet Union, the ensuing financial crisis meant the Russians could no longer afford to undertake simultaneous development of two carrier-borne aircrafts, under two different programmes. Thus, the Sukhoi Design Bureau's Su-33 fighter [Su-27K] was, eventually, chosen to equip its sole Aircraft Carrier, the Admiral Kuznetsov, and the MiG-29K/KUB programme was, for all practical purposes, mothballed.
Till the the Indian Navy evinced interest in it, that is. Thus, it wouldn't be completely off the mark to state that the Indian Navy effectively financed the completion of its development programme, that includes setting up/adaption of the production line with the tooling needed to make these birds for its own requirements. They are expected to serve as the frontline aircraft of the Indian Navy, operating off the Aircraft Carrier INS Vikramditya [Ex-Admiral Gorshkov], as well as the first indigenously developed Indian Aircraft Carrier [IAC-1 a.k.a INS Vikrant]. In fact, with the development now complete & production up & running, the Russians too have gone ahead & placed orders to acquire these aircrafts for its own Navy. While this could not be the sole reason, that fact that you have an aircraft whose development cycle has finished just recently & is considered to be potent platform, would surely have played some role in the buying decision.
A collection of pictures, below, shows an initial design iteration of the MiG-29K being put through its paces on-board the Kuznetsov in the 1991, prior to the demise of the U.S.S.R., much like the recent times.
click on the image to view them in larger size
via МиГ 29 КУБ вместо СУ-33 ? || Мировой парад "ниток"
Godspeed
Related: Report: MiG-29K/KUB flight test from aboard Indian Navy Aircraft Carrier INS Vikramaditya