Most of the major navies will only deploy twin engine aircraft on their carriers. The only exception has been F-35 and it carries a very powerful single engine. Even so its maneuverability is poor under load.
There are only a handful of navies with aircraft carriers. Majority of the new naval airframes will be F-35 B/C.
- USN -> F-35C & (mostly already in-service) F/A-18 E/F/G
- USMC -> F-35B/C
- RN -> F-35B
- ItN -> F-35B
- FrN -> Rafale
- RuN -> MiG-29K
- IN -> MiG-29K
- PLAN -> Su-33 clone
In a decade, the choices for naval fighter will dwindle to F-35 B/C and Su-33 clone. NLCA Mk.2 would be the other. Plus, other UCAVs maybe entering service around that time. NAMCA would come a little bit later.
So all indication for the IN wanting 57 foreign naval fighter "soon" points to F-35B, which would be compatible with its two STOBAR carriers. The RN has been qualifying F-35B for its own two STOBAR carriers.